Applied_Quant_Finance.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Kopie van Applied Quant Finance.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "toc_visible": true
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "PfFjYzx5vBlI",
        "outputId": "ecf8c869-e395-456c-9164-e8f717146268"
      },
      "source": [
        "#Imports\n",
        "import pandas as pd\n",
        "from numpy import savetxt\n",
        "import numpy as np\n",
        "import time\n",
        "from datetime import datetime,timedelta\n",
        "import math\n",
        "import scipy\n",
        "import scipy.integrate as integrate\n",
        "import scipy.sparse as sparse\n",
        "from scipy.linalg import lu_factor, lu_solve\n",
        "!pip install arch\n",
        "import arch\n",
        "from sklearn.linear_model import LinearRegression\n",
        "from sklearn.svm import SVR\n",
        "\n",
        "import tensorflow as tf\n",
        "import tensorflow_probability as tfp\n",
        "import keras\n",
        "from tensorflow.keras.models import Sequential\n",
        "from tensorflow.keras.layers import Dense\n",
        "\n",
        "from google.colab import drive\n",
        "from google.colab import files\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.ndimage.interpolation import shift\n",
        "\n",
        "from sympy.solvers import solve\n",
        "from sympy import Symbol\n",
        "from scipy.stats import norm\n",
        "\n",
        "import decimal\n",
        "import itertools"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Collecting arch\n",
            "\u001b[?25l  Downloading https://files.pythonhosted.org/packages/5f/a8/a85dad77039d2884547d4fb83d54edfc13a12e31981934d6d0fb6303b791/arch-4.19-cp37-cp37m-manylinux1_x86_64.whl (807kB)\n",
            "\r\u001b[K     |▍                               | 10kB 13.7MB/s eta 0:00:01\r\u001b[K     |▉                               | 20kB 19.9MB/s eta 0:00:01\r\u001b[K     |█▏                              | 30kB 16.7MB/s eta 0:00:01\r\u001b[K     |█▋                              | 40kB 12.4MB/s eta 0:00:01\r\u001b[K     |██                              | 51kB 5.1MB/s eta 0:00:01\r\u001b[K     |██▍                             | 61kB 5.7MB/s eta 0:00:01\r\u001b[K     |██▉                             | 71kB 6.1MB/s eta 0:00:01\r\u001b[K     |███▎                            | 81kB 6.4MB/s eta 0:00:01\r\u001b[K     |███▋                            | 92kB 6.8MB/s eta 0:00:01\r\u001b[K     |████                            | 102kB 7.1MB/s eta 0:00:01\r\u001b[K     |████▌                           | 112kB 7.1MB/s eta 0:00:01\r\u001b[K     |████▉                           | 122kB 7.1MB/s eta 0:00:01\r\u001b[K     |█████▎                          | 133kB 7.1MB/s eta 0:00:01\r\u001b[K     |█████▊                          | 143kB 7.1MB/s eta 0:00:01\r\u001b[K     |██████                          | 153kB 7.1MB/s eta 0:00:01\r\u001b[K     |██████▌                         | 163kB 7.1MB/s eta 0:00:01\r\u001b[K     |███████                         | 174kB 7.1MB/s eta 0:00:01\r\u001b[K     |███████▎                        | 184kB 7.1MB/s eta 0:00:01\r\u001b[K     |███████▊                        | 194kB 7.1MB/s eta 0:00:01\r\u001b[K     |████████▏                       | 204kB 7.1MB/s eta 0:00:01\r\u001b[K     |████████▌                       | 215kB 7.1MB/s eta 0:00:01\r\u001b[K     |█████████                       | 225kB 7.1MB/s eta 0:00:01\r\u001b[K     |█████████▍                      | 235kB 7.1MB/s eta 0:00:01\r\u001b[K     |█████████▊                      | 245kB 7.1MB/s eta 0:00:01\r\u001b[K     |██████████▏                     | 256kB 7.1MB/s eta 0:00:01\r\u001b[K     |██████████▌                     | 266kB 7.1MB/s eta 0:00:01\r\u001b[K     |███████████                     | 276kB 7.1MB/s eta 0:00:01\r\u001b[K     |███████████▍                    | 286kB 7.1MB/s eta 0:00:01\r\u001b[K     |███████████▊                    | 296kB 7.1MB/s eta 0:00:01\r\u001b[K     |████████████▏                   | 307kB 7.1MB/s eta 0:00:01\r\u001b[K     |████████████▋                   | 317kB 7.1MB/s eta 0:00:01\r\u001b[K     |█████████████                   | 327kB 7.1MB/s eta 0:00:01\r\u001b[K     |█████████████▍                  | 337kB 7.1MB/s eta 0:00:01\r\u001b[K     |█████████████▉                  | 348kB 7.1MB/s eta 0:00:01\r\u001b[K     |██████████████▏                 | 358kB 7.1MB/s eta 0:00:01\r\u001b[K     |██████████████▋                 | 368kB 7.1MB/s eta 0:00:01\r\u001b[K     |███████████████                 | 378kB 7.1MB/s eta 0:00:01\r\u001b[K     |███████████████▍                | 389kB 7.1MB/s eta 0:00:01\r\u001b[K     |███████████████▉                | 399kB 7.1MB/s eta 0:00:01\r\u001b[K     |████████████████▎               | 409kB 7.1MB/s eta 0:00:01\r\u001b[K     |████████████████▋               | 419kB 7.1MB/s eta 0:00:01\r\u001b[K     |█████████████████               | 430kB 7.1MB/s eta 0:00:01\r\u001b[K     |█████████████████▌              | 440kB 7.1MB/s eta 0:00:01\r\u001b[K     |█████████████████▉              | 450kB 7.1MB/s eta 0:00:01\r\u001b[K     |██████████████████▎             | 460kB 7.1MB/s eta 0:00:01\r\u001b[K     |██████████████████▊             | 471kB 7.1MB/s eta 0:00:01\r\u001b[K     |███████████████████             | 481kB 7.1MB/s eta 0:00:01\r\u001b[K     |███████████████████▌            | 491kB 7.1MB/s eta 0:00:01\r\u001b[K     |████████████████████            | 501kB 7.1MB/s eta 0:00:01\r\u001b[K     |████████████████████▎           | 512kB 7.1MB/s eta 0:00:01\r\u001b[K     |████████████████████▊           | 522kB 7.1MB/s eta 0:00:01\r\u001b[K     |█████████████████████           | 532kB 7.1MB/s eta 0:00:01\r\u001b[K     |█████████████████████▌          | 542kB 7.1MB/s eta 0:00:01\r\u001b[K     |██████████████████████          | 552kB 7.1MB/s eta 0:00:01\r\u001b[K     |██████████████████████▎         | 563kB 7.1MB/s eta 0:00:01\r\u001b[K     |██████████████████████▊         | 573kB 7.1MB/s eta 0:00:01\r\u001b[K     |███████████████████████▏        | 583kB 7.1MB/s eta 0:00:01\r\u001b[K     |███████████████████████▌        | 593kB 7.1MB/s eta 0:00:01\r\u001b[K     |████████████████████████        | 604kB 7.1MB/s eta 0:00:01\r\u001b[K     |████████████████████████▍       | 614kB 7.1MB/s eta 0:00:01\r\u001b[K     |████████████████████████▊       | 624kB 7.1MB/s eta 0:00:01\r\u001b[K     |█████████████████████████▏      | 634kB 7.1MB/s eta 0:00:01\r\u001b[K     |█████████████████████████▋      | 645kB 7.1MB/s eta 0:00:01\r\u001b[K     |██████████████████████████      | 655kB 7.1MB/s eta 0:00:01\r\u001b[K     |██████████████████████████▍     | 665kB 7.1MB/s eta 0:00:01\r\u001b[K     |██████████████████████████▉     | 675kB 7.1MB/s eta 0:00:01\r\u001b[K     |███████████████████████████▏    | 686kB 7.1MB/s eta 0:00:01\r\u001b[K     |███████████████████████████▋    | 696kB 7.1MB/s eta 0:00:01\r\u001b[K     |████████████████████████████    | 706kB 7.1MB/s eta 0:00:01\r\u001b[K     |████████████████████████████▍   | 716kB 7.1MB/s eta 0:00:01\r\u001b[K     |████████████████████████████▉   | 727kB 7.1MB/s eta 0:00:01\r\u001b[K     |█████████████████████████████▎  | 737kB 7.1MB/s eta 0:00:01\r\u001b[K     |█████████████████████████████▋  | 747kB 7.1MB/s eta 0:00:01\r\u001b[K     |██████████████████████████████  | 757kB 7.1MB/s eta 0:00:01\r\u001b[K     |██████████████████████████████▌ | 768kB 7.1MB/s eta 0:00:01\r\u001b[K     |██████████████████████████████▉ | 778kB 7.1MB/s eta 0:00:01\r\u001b[K     |███████████████████████████████▎| 788kB 7.1MB/s eta 0:00:01\r\u001b[K     |███████████████████████████████▋| 798kB 7.1MB/s eta 0:00:01\r\u001b[K     |████████████████████████████████| 808kB 7.1MB/s \n",
            "\u001b[?25hRequirement already satisfied: cython>=0.29.14 in /usr/local/lib/python3.7/dist-packages (from arch) (0.29.22)\n",
            "Requirement already satisfied: statsmodels>=0.10 in /usr/local/lib/python3.7/dist-packages (from arch) (0.10.2)\n",
            "Collecting property-cached>=1.6.4\n",
            "  Downloading https://files.pythonhosted.org/packages/5c/6c/94d8e520b20a2502e508e1c558f338061cf409cbee78fd6a3a5c6ae812bd/property_cached-1.6.4-py2.py3-none-any.whl\n",
            "Requirement already satisfied: pandas>=0.23 in /usr/local/lib/python3.7/dist-packages (from arch) (1.1.5)\n",
            "Requirement already satisfied: numpy>=1.14 in /usr/local/lib/python3.7/dist-packages (from arch) (1.19.5)\n",
            "Requirement already satisfied: scipy>=1.2.3 in /usr/local/lib/python3.7/dist-packages (from arch) (1.4.1)\n",
            "Requirement already satisfied: patsy>=0.4.0 in /usr/local/lib/python3.7/dist-packages (from statsmodels>=0.10->arch) (0.5.1)\n",
            "Requirement already satisfied: python-dateutil>=2.7.3 in /usr/local/lib/python3.7/dist-packages (from pandas>=0.23->arch) (2.8.1)\n",
            "Requirement already satisfied: pytz>=2017.2 in /usr/local/lib/python3.7/dist-packages (from pandas>=0.23->arch) (2018.9)\n",
            "Requirement already satisfied: six in /usr/local/lib/python3.7/dist-packages (from patsy>=0.4.0->statsmodels>=0.10->arch) (1.15.0)\n",
            "Installing collected packages: property-cached, arch\n",
            "Successfully installed arch-4.19 property-cached-1.6.4\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/statsmodels/tools/_testing.py:19: FutureWarning: pandas.util.testing is deprecated. Use the functions in the public API at pandas.testing instead.\n",
            "  import pandas.util.testing as tm\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5o2zhoud9QSw"
      },
      "source": [
        "# Data Processing"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QJKSPSVXw09C"
      },
      "source": [
        "OEX: SECID 109764\n",
        "XEO: SECID 112878"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "60AaqfgHvw7_",
        "outputId": "22c10c2b-9fc5-4c9d-cc09-d26c4ff70b77"
      },
      "source": [
        "drive.mount('/content/drive')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Mounted at /content/drive\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "H_WVtcFtzTQb"
      },
      "source": [
        "option_data = pd.read_csv('/content/drive/MyDrive/data aqf/oex option data 2000-2020.csv')\n",
        "underlying_data=pd.read_csv('/content/drive/MyDrive/data aqf/oex underlying.csv')\n",
        "vix_data=pd.read_csv('/content/drive/MyDrive/data aqf/vix index.csv')\n",
        "interest_rate_data=pd.read_csv('/content/drive/MyDrive/data aqf/yield curve.csv')\n",
        "option_data_european = pd.read_csv('/content/drive/MyDrive/data aqf/xeo option data 2002-2020.csv')\n",
        "underlying_data[['numerical_date']] = underlying_data['date']\n",
        "underlying_data[['date']] = pd.to_datetime(underlying_data['date'],format='%Y%m%d')\n",
        "underlying_data['date'] = underlying_data[\"date\"].dt.date\n",
        "vix_data[['date']] = pd.to_datetime(vix_data['Date'],format='%Y%m%d')\n",
        "vix_data['date'] = vix_data[\"date\"].dt.date\n",
        "interest_rate_data[['date']] = pd.to_datetime(interest_rate_data['date'],format='%Y%m%d')\n",
        "interest_rate_data['date'] = interest_rate_data[\"date\"].dt.date"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JNUeV7qb9Vs6"
      },
      "source": [
        "# Data Cleaning"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "h87KMYkVxncH"
      },
      "source": [
        "def process_data(option_data,underlying_data,interest_rate_data,vix_data,is_American):\n",
        "  option_data[['numerical_date']] = option_data['date']\n",
        "  #Remove options with the wrong date\n",
        "  min_date=20030101\n",
        "  max_date=20121231\n",
        "  option_data=option_data[(option_data['date'] >= min_date) & (option_data['date'] <= max_date)]\n",
        " \n",
        "  #Remove options below a certain volume\n",
        "  min_volume=1\n",
        "  option_data=option_data[option_data['volume'] >= min_volume]\n",
        " \n",
        "  #Remove call options\n",
        "  option_data=option_data[ option_data['cp_flag'] == \"P\" ]\n",
        " \n",
        "  #Create a time to maturity column (in trading days)\n",
        "  option_data[['date']] = pd.to_datetime(option_data['date'],format='%Y%m%d')\n",
        "  option_data['date'] = option_data[\"date\"].dt.date\n",
        "  option_data[['exdate']] = pd.to_datetime(option_data['exdate'],format='%Y%m%d')\n",
        "  option_data['exdate'] = option_data[\"exdate\"].dt.date\n",
        "  if(is_American):\n",
        "    option_data[['last_date']] = pd.to_datetime(option_data['last_date'],format='%Y%m%d')\n",
        "    option_data['last_date'] = option_data[\"last_date\"].dt.date\n",
        "  option_data['maturity']=np.busday_count(option_data['date'],option_data['exdate'], weekmask='1111111') #Do we have to include weekends?\n",
        " \n",
        "  #Remove options that do not have correct maturity\n",
        "  min_maturity=7\n",
        "  max_maturity=90\n",
        "  option_data = option_data[(option_data['maturity'] <= max_maturity) & (option_data['maturity'] >= min_maturity)]\n",
        " \n",
        "  #Create a column with market prices\n",
        "  option_data['market price'] = (option_data['best_bid'] + option_data['best_offer'])/2\n",
        " \n",
        "  #Add the underlying to the dataframe\n",
        "  rows=option_data.shape[0]\n",
        "  underlying_vec=np.empty(rows, dtype=object)\n",
        "  date_selector=0\n",
        "  row_number=0\n",
        "  for index, row in option_data.iterrows():\n",
        "    while (underlying_data.at[date_selector,'date']!=row['date']):\n",
        "      date_selector=date_selector+1\n",
        "    underlying_vec[row_number]=underlying_data.at[date_selector,'close']\n",
        "    row_number=row_number+1\n",
        "  option_data['underlying']=underlying_vec\n",
        " \n",
        "  #Create columns moneyness and time value\n",
        "  option_data['moneyness'] = option_data['underlying'] / option_data['strike_price'] * 1000\n",
        "  option_data['time value'] =  option_data['market price'] - (option_data['strike_price']/1000 - option_data['underlying'])\n",
        " \n",
        "  #Create column with forward volume\n",
        "  option_data['1d forward volume'] = option_data.groupby(['optionid'])['volume'].shift(-1)\n",
        " \n",
        "  #Cleaning based on Ruf and Wang 2020 (https://github.com/weiguanwang/Hedging_Neural_Networks/tree/74d5a7b72626e92395d056ced01cb8e135edcbcc)\n",
        "  option_data.dropna(subset=['impl_volatility'], how='any', inplace=True)\n",
        "  option_data = option_data[(option_data['impl_volatility'] < 1) & (option_data['impl_volatility'] > 0.01)] \n",
        "  option_data = option_data[option_data['volume'] > 0]\n",
        "  option_data = option_data[option_data['best_bid'] > 0.05]\n",
        "  option_data = option_data[(option_data['time value']> 0)]\n",
        "  option_data = option_data[ (2*option_data['best_bid'] > option_data['best_offer'])]\n",
        "  option_data = option_data[~option_data['1d forward volume'].isna()]\n",
        "  if(is_American):\n",
        "    option_data = option_data[option_data['last_date'] == option_data['date']]\n",
        " \n",
        "  if (is_American):\n",
        "    #Add the VIX to the dataframe\n",
        "    rows=option_data.shape[0]\n",
        "    vix_vec=np.empty(rows, dtype=object)\n",
        "    date_selector=0\n",
        "    row_number=0\n",
        "    for index, row in option_data.iterrows():\n",
        "      while (vix_data.at[date_selector,'date']!=row['date']):\n",
        "        date_selector=date_selector+1\n",
        "      vix_vec[row_number]=vix_data.at[date_selector,'vxo']\n",
        "      if isinstance(vix_vec[row_number], (int, float, complex)):\n",
        "        1+1\n",
        "      else:\n",
        "        print(\"no number \" + str(vix_vec[row_number]))\n",
        "      row_number=row_number+1\n",
        "    option_data['vix']=vix_vec\n",
        " \n",
        "  #Add the interest to the dataframe -> maybe should scale it somehow\n",
        "  rows=option_data.shape[0]\n",
        "  interest_rate_vec=np.empty(rows, dtype=object)\n",
        "  date_selector=0\n",
        "  row_number=0\n",
        "  for index, row in option_data.iterrows():\n",
        "    while (interest_rate_data.at[date_selector,'date']<row['date']): #There are dates where options are traded, but no interest is quoted\n",
        "      date_selector=date_selector+1\n",
        "      if date_selector>=216968:\n",
        "        print(date_selector)\n",
        "        print(interest_rate_data.at[date_selector,'date'])\n",
        "        print(row['date'])\n",
        "    i=0\n",
        "    while (interest_rate_data.at[date_selector+i,'days']<row['maturity']):\n",
        "      i=i+1\n",
        "    left_gap=row['maturity']-interest_rate_data.at[date_selector+i-1,'days']\n",
        "    right_gap=interest_rate_data.at[date_selector+i,'days']-row['maturity']\n",
        "    if left_gap<right_gap:\n",
        "      i=i-1\n",
        "    interest_rate_vec[row_number]=interest_rate_data.at[date_selector+i,'rate']\n",
        "    row_number=row_number+1\n",
        "  option_data['interest_rate']=interest_rate_vec\n",
        " \n",
        "  option_data['maturity']=option_data['maturity']/250\n",
        "  option_data['strike_price']=option_data['strike_price']/1000\n",
        " \n",
        "  return option_data"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 388
        },
        "id": "BVvnES-pPYmo",
        "outputId": "c3e7a641-57d5-45b1-b1df-56b32f6e3997"
      },
      "source": [
        "option_data=process_data(option_data,underlying_data,interest_rate_data,vix_data,True)\n",
        "option_data_european=process_data(option_data_european,underlying_data,interest_rate_data,vix_data,False)\n",
        "option_data"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>secid</th>\n",
              "      <th>date</th>\n",
              "      <th>exdate</th>\n",
              "      <th>last_date</th>\n",
              "      <th>cp_flag</th>\n",
              "      <th>strike_price</th>\n",
              "      <th>best_bid</th>\n",
              "      <th>best_offer</th>\n",
              "      <th>volume</th>\n",
              "      <th>impl_volatility</th>\n",
              "      <th>optionid</th>\n",
              "      <th>forward_price</th>\n",
              "      <th>index_flag</th>\n",
              "      <th>issuer</th>\n",
              "      <th>exercise_style</th>\n",
              "      <th>numerical_date</th>\n",
              "      <th>maturity</th>\n",
              "      <th>market price</th>\n",
              "      <th>underlying</th>\n",
              "      <th>moneyness</th>\n",
              "      <th>time value</th>\n",
              "      <th>1d forward volume</th>\n",
              "      <th>vix</th>\n",
              "      <th>interest_rate</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>215739</th>\n",
              "      <td>109764</td>\n",
              "      <td>2003-01-02</td>\n",
              "      <td>2003-01-18</td>\n",
              "      <td>2003-01-02</td>\n",
              "      <td>P</td>\n",
              "      <td>500.0</td>\n",
              "      <td>41.30</td>\n",
              "      <td>42.80</td>\n",
              "      <td>2</td>\n",
              "      <td>0.323715</td>\n",
              "      <td>20842600</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1</td>\n",
              "      <td>CBOE S&amp;P 100 INDEX</td>\n",
              "      <td>A</td>\n",
              "      <td>20030102</td>\n",
              "      <td>0.064</td>\n",
              "      <td>42.050</td>\n",
              "      <td>459.5</td>\n",
              "      <td>0.919</td>\n",
              "      <td>1.55</td>\n",
              "      <td>4.0</td>\n",
              "      <td>28.52</td>\n",
              "      <td>1.37095</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>215800</th>\n",
              "      <td>109764</td>\n",
              "      <td>2003-01-02</td>\n",
              "      <td>2003-01-18</td>\n",
              "      <td>2003-01-02</td>\n",
              "      <td>P</td>\n",
              "      <td>370.0</td>\n",
              "      <td>0.10</td>\n",
              "      <td>0.15</td>\n",
              "      <td>330</td>\n",
              "      <td>0.456722</td>\n",
              "      <td>20873060</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1</td>\n",
              "      <td>CBOE S&amp;P 100 INDEX</td>\n",
              "      <td>A</td>\n",
              "      <td>20030102</td>\n",
              "      <td>0.064</td>\n",
              "      <td>0.125</td>\n",
              "      <td>459.5</td>\n",
              "      <td>1.24189</td>\n",
              "      <td>89.625</td>\n",
              "      <td>155.0</td>\n",
              "      <td>28.52</td>\n",
              "      <td>1.37095</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>215805</th>\n",
              "      <td>109764</td>\n",
              "      <td>2003-01-02</td>\n",
              "      <td>2003-02-22</td>\n",
              "      <td>2003-01-02</td>\n",
              "      <td>P</td>\n",
              "      <td>340.0</td>\n",
              "      <td>0.55</td>\n",
              "      <td>0.85</td>\n",
              "      <td>17</td>\n",
              "      <td>0.428497</td>\n",
              "      <td>20873063</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1</td>\n",
              "      <td>CBOE S&amp;P 100 INDEX</td>\n",
              "      <td>A</td>\n",
              "      <td>20030102</td>\n",
              "      <td>0.204</td>\n",
              "      <td>0.700</td>\n",
              "      <td>459.5</td>\n",
              "      <td>1.35147</td>\n",
              "      <td>120.2</td>\n",
              "      <td>49.0</td>\n",
              "      <td>28.52</td>\n",
              "      <td>1.39453</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>215807</th>\n",
              "      <td>109764</td>\n",
              "      <td>2003-01-02</td>\n",
              "      <td>2003-02-22</td>\n",
              "      <td>2003-01-02</td>\n",
              "      <td>P</td>\n",
              "      <td>360.0</td>\n",
              "      <td>1.05</td>\n",
              "      <td>1.45</td>\n",
              "      <td>300</td>\n",
              "      <td>0.399460</td>\n",
              "      <td>20873064</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1</td>\n",
              "      <td>CBOE S&amp;P 100 INDEX</td>\n",
              "      <td>A</td>\n",
              "      <td>20030102</td>\n",
              "      <td>0.204</td>\n",
              "      <td>1.250</td>\n",
              "      <td>459.5</td>\n",
              "      <td>1.27639</td>\n",
              "      <td>100.75</td>\n",
              "      <td>54.0</td>\n",
              "      <td>28.52</td>\n",
              "      <td>1.39453</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>215808</th>\n",
              "      <td>109764</td>\n",
              "      <td>2003-01-02</td>\n",
              "      <td>2003-02-22</td>\n",
              "      <td>2003-01-02</td>\n",
              "      <td>P</td>\n",
              "      <td>370.0</td>\n",
              "      <td>1.45</td>\n",
              "      <td>1.85</td>\n",
              "      <td>39</td>\n",
              "      <td>0.384597</td>\n",
              "      <td>21341739</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1</td>\n",
              "      <td>CBOE S&amp;P 100 INDEX</td>\n",
              "      <td>A</td>\n",
              "      <td>20030102</td>\n",
              "      <td>0.204</td>\n",
              "      <td>1.650</td>\n",
              "      <td>459.5</td>\n",
              "      <td>1.24189</td>\n",
              "      <td>91.15</td>\n",
              "      <td>15.0</td>\n",
              "      <td>28.52</td>\n",
              "      <td>1.39453</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1264305</th>\n",
              "      <td>109764</td>\n",
              "      <td>2012-12-28</td>\n",
              "      <td>2013-02-16</td>\n",
              "      <td>2012-12-28</td>\n",
              "      <td>P</td>\n",
              "      <td>620.0</td>\n",
              "      <td>11.50</td>\n",
              "      <td>12.30</td>\n",
              "      <td>7</td>\n",
              "      <td>0.198526</td>\n",
              "      <td>83448206</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1</td>\n",
              "      <td>CBOE S&amp;P 100 INDEX</td>\n",
              "      <td>A</td>\n",
              "      <td>20121228</td>\n",
              "      <td>0.200</td>\n",
              "      <td>11.900</td>\n",
              "      <td>636.17</td>\n",
              "      <td>1.02608</td>\n",
              "      <td>28.07</td>\n",
              "      <td>37.0</td>\n",
              "      <td>23.07</td>\n",
              "      <td>0.274633</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1264306</th>\n",
              "      <td>109764</td>\n",
              "      <td>2012-12-28</td>\n",
              "      <td>2013-02-16</td>\n",
              "      <td>2012-12-28</td>\n",
              "      <td>P</td>\n",
              "      <td>640.0</td>\n",
              "      <td>18.90</td>\n",
              "      <td>19.80</td>\n",
              "      <td>2</td>\n",
              "      <td>0.176025</td>\n",
              "      <td>83448207</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1</td>\n",
              "      <td>CBOE S&amp;P 100 INDEX</td>\n",
              "      <td>A</td>\n",
              "      <td>20121228</td>\n",
              "      <td>0.200</td>\n",
              "      <td>19.350</td>\n",
              "      <td>636.17</td>\n",
              "      <td>0.994016</td>\n",
              "      <td>15.52</td>\n",
              "      <td>66.0</td>\n",
              "      <td>23.07</td>\n",
              "      <td>0.274633</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1264307</th>\n",
              "      <td>109764</td>\n",
              "      <td>2012-12-28</td>\n",
              "      <td>2013-02-16</td>\n",
              "      <td>2012-12-28</td>\n",
              "      <td>P</td>\n",
              "      <td>660.0</td>\n",
              "      <td>29.30</td>\n",
              "      <td>31.50</td>\n",
              "      <td>7</td>\n",
              "      <td>0.148371</td>\n",
              "      <td>83448208</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1</td>\n",
              "      <td>CBOE S&amp;P 100 INDEX</td>\n",
              "      <td>A</td>\n",
              "      <td>20121228</td>\n",
              "      <td>0.200</td>\n",
              "      <td>30.400</td>\n",
              "      <td>636.17</td>\n",
              "      <td>0.963894</td>\n",
              "      <td>6.57</td>\n",
              "      <td>10.0</td>\n",
              "      <td>23.07</td>\n",
              "      <td>0.274633</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1264338</th>\n",
              "      <td>109764</td>\n",
              "      <td>2012-12-28</td>\n",
              "      <td>2013-03-16</td>\n",
              "      <td>2012-12-28</td>\n",
              "      <td>P</td>\n",
              "      <td>640.0</td>\n",
              "      <td>23.50</td>\n",
              "      <td>24.40</td>\n",
              "      <td>3</td>\n",
              "      <td>0.175640</td>\n",
              "      <td>83151400</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1</td>\n",
              "      <td>CBOE S&amp;P 100 INDEX</td>\n",
              "      <td>A</td>\n",
              "      <td>20121228</td>\n",
              "      <td>0.312</td>\n",
              "      <td>23.950</td>\n",
              "      <td>636.17</td>\n",
              "      <td>0.994016</td>\n",
              "      <td>20.12</td>\n",
              "      <td>1.0</td>\n",
              "      <td>23.07</td>\n",
              "      <td>0.288166</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1264339</th>\n",
              "      <td>109764</td>\n",
              "      <td>2012-12-28</td>\n",
              "      <td>2013-03-16</td>\n",
              "      <td>2012-12-28</td>\n",
              "      <td>P</td>\n",
              "      <td>660.0</td>\n",
              "      <td>34.30</td>\n",
              "      <td>35.50</td>\n",
              "      <td>1</td>\n",
              "      <td>0.157624</td>\n",
              "      <td>83151401</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1</td>\n",
              "      <td>CBOE S&amp;P 100 INDEX</td>\n",
              "      <td>A</td>\n",
              "      <td>20121228</td>\n",
              "      <td>0.312</td>\n",
              "      <td>34.900</td>\n",
              "      <td>636.17</td>\n",
              "      <td>0.963894</td>\n",
              "      <td>11.07</td>\n",
              "      <td>6.0</td>\n",
              "      <td>23.07</td>\n",
              "      <td>0.288166</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>103496 rows × 24 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "          secid        date      exdate  ... 1d forward volume    vix  interest_rate\n",
              "215739   109764  2003-01-02  2003-01-18  ...               4.0  28.52        1.37095\n",
              "215800   109764  2003-01-02  2003-01-18  ...             155.0  28.52        1.37095\n",
              "215805   109764  2003-01-02  2003-02-22  ...              49.0  28.52        1.39453\n",
              "215807   109764  2003-01-02  2003-02-22  ...              54.0  28.52        1.39453\n",
              "215808   109764  2003-01-02  2003-02-22  ...              15.0  28.52        1.39453\n",
              "...         ...         ...         ...  ...               ...    ...            ...\n",
              "1264305  109764  2012-12-28  2013-02-16  ...              37.0  23.07       0.274633\n",
              "1264306  109764  2012-12-28  2013-02-16  ...              66.0  23.07       0.274633\n",
              "1264307  109764  2012-12-28  2013-02-16  ...              10.0  23.07       0.274633\n",
              "1264338  109764  2012-12-28  2013-03-16  ...               1.0  23.07       0.288166\n",
              "1264339  109764  2012-12-28  2013-03-16  ...               6.0  23.07       0.288166\n",
              "\n",
              "[103496 rows x 24 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iJDIU1eDjidV"
      },
      "source": [
        "# Tables data\n",
        "\n",
        "Code that creates tables that describe summary statistics of the data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "VBrLS4rviUSC",
        "outputId": "2a4f46fe-b181-43d5-ff61-7229ce1ff41e"
      },
      "source": [
        "moneyness_vec=np.array([0.94,0.97,1,1.03,1.06])\n",
        "maturity_vec=np.array([30,60])/250\n",
        "mean_matrix=np.zeros([len(moneyness_vec)+2,len(maturity_vec)+2])\n",
        "sd_matrix=np.zeros([len(moneyness_vec)+2,len(maturity_vec)+2])\n",
        "amount_matrix=np.zeros([len(moneyness_vec)+2,len(maturity_vec)+2])\n",
        "\n",
        "for m in range(0,len(moneyness_vec)+2):\n",
        "  for t in range(0,len(maturity_vec)+2):\n",
        "    if (m==0):\n",
        "      moneyness_lower_bound=0\n",
        "      moneyness_upper_bound=moneyness_vec[m]\n",
        "    if (m>0 and m<len(moneyness_vec)):\n",
        "      moneyness_lower_bound=moneyness_vec[m-1]\n",
        "      moneyness_upper_bound=moneyness_vec[m]\n",
        "    if (m==len(moneyness_vec)):\n",
        "      moneyness_lower_bound=moneyness_vec[m-1]\n",
        "      moneyness_upper_bound=10**8\n",
        "    if (m==len(moneyness_vec)+1):\n",
        "      moneyness_lower_bound=0\n",
        "      moneyness_upper_bound=10**8\n",
        "    if (t==0):\n",
        "      maturity_lower_bound=0\n",
        "      maturity_upper_bound=maturity_vec[t]\n",
        "    if (t>0 and t<len(maturity_vec)):\n",
        "      maturity_lower_bound=maturity_vec[t-1]\n",
        "      maturity_upper_bound=maturity_vec[t]\n",
        "    if (t==len(maturity_vec)):\n",
        "      maturity_lower_bound=maturity_vec[t-1]\n",
        "      maturity_upper_bound=10**8\n",
        "    if (t==len(maturity_vec)+1):\n",
        "      maturity_lower_bound=0\n",
        "      maturity_upper_bound=10**8\n",
        "    options=option_data[(option_data['maturity'] >= maturity_lower_bound) & (option_data['maturity'] <= maturity_upper_bound) & (option_data['moneyness'] >= moneyness_lower_bound) & (option_data['moneyness'] <= moneyness_upper_bound)]\n",
        "    mean_matrix[m,t]=np.mean(options['market price'])\n",
        "    sd_matrix[m,t]=np.std(options['market price'])\n",
        "    amount_matrix[m,t]=len(options['market price'])\n",
        "mean_matrix=np.around(mean_matrix,2)\n",
        "sd_matrix=np.around(sd_matrix,2)\n",
        "amount_matrix=np.around(amount_matrix,0)\n",
        "\n",
        "for m in range(0,len(moneyness_vec)+2):\n",
        "  for t in range(0,len(maturity_vec)+2):\n",
        "    if (t==0):\n",
        "      print(\" & Price & \" + str(mean_matrix[m,t]) + \" & \" + str(sd_matrix[m,t]) + \" & \", end =\" \")\n",
        "    elif (t==len(maturity_vec)+1):\n",
        "      print(str(mean_matrix[m,t]) + \" & \" + str(sd_matrix[m,t]), end =\" \")\n",
        "    else: \n",
        "      print(str(mean_matrix[m,t]) + \" & \" + str(sd_matrix[m,t]) + \" & \", end =\" \")\n",
        "  print(\"\\\\\" + \"\\\\\")\n",
        "  for t in range(0,len(maturity_vec)+2):\n",
        "    if (t==0):\n",
        "      print(\" & Observations & \" + str(int(amount_matrix[m,t])) + \" & & \", end =\" \")\n",
        "    elif (t==len(maturity_vec)+1):\n",
        "      print(str(int(amount_matrix[m,t])) + \" & \", end =\" \")\n",
        "    else:\n",
        "      print(str(int(amount_matrix[m,t])) + \" & & \", end =\" \")\n",
        "  print(\"\\\\\" + \"\\\\\")\n",
        "\n",
        "print()\n",
        "\n",
        "year_vec=np.array([2003,2004,2005,2006,2007,2008,2009,2010,2011,2012])\n",
        "moneyness_vec=np.array([0.97,1.03])\n",
        "maturity_vec=np.array([30,60])/250\n",
        "amount_matrix_moneyness=np.zeros([len(year_vec),len(moneyness_vec)+1])\n",
        "amount_matrix_maturity=np.zeros([len(year_vec),len(maturity_vec)+2])\n",
        "for m in range(0,len(moneyness_vec)+1):\n",
        "  for y in range(0,len(year_vec)):\n",
        "    if (m==0):\n",
        "      moneyness_lower_bound=0\n",
        "      moneyness_upper_bound=moneyness_vec[m]\n",
        "    if (m>0 and m<len(moneyness_vec)):\n",
        "      moneyness_lower_bound=moneyness_vec[m-1]\n",
        "      moneyness_upper_bound=moneyness_vec[m]\n",
        "    if (m==len(moneyness_vec)):\n",
        "      moneyness_lower_bound=moneyness_vec[m-1]\n",
        "      moneyness_upper_bound=10**8\n",
        "    options=option_data[(option_data['numerical_date'] >= year_vec[y]*10**4) & (option_data['numerical_date'] < (year_vec[y]+1)*10**4) & (option_data['moneyness'] >= moneyness_lower_bound) & (option_data['moneyness'] < moneyness_upper_bound)]\n",
        "    amount_matrix_moneyness[y,m]=len(options['market price'])\n",
        "for t in range(0,len(maturity_vec)+2):\n",
        "  for y in range(0,len(year_vec)):\n",
        "    if (t==0):\n",
        "      maturity_lower_bound=0\n",
        "      maturity_upper_bound=maturity_vec[t]\n",
        "    if (t>0 and t<len(maturity_vec)):\n",
        "      maturity_lower_bound=maturity_vec[t-1]-(1/250)+(1/1000)\n",
        "      maturity_upper_bound=maturity_vec[t]+(1/250)-(1/1000)\n",
        "    if (t==len(maturity_vec)):\n",
        "      maturity_lower_bound=maturity_vec[t-1]\n",
        "      maturity_upper_bound=10**8\n",
        "    if (t==len(maturity_vec)+1):\n",
        "      maturity_lower_bound=0\n",
        "      maturity_upper_bound=10**8\n",
        "    options=option_data[(option_data['numerical_date'] >= year_vec[y]*10**4) & (option_data['numerical_date'] < (year_vec[y]+1)*10**4) & (option_data['maturity'] > maturity_lower_bound) & (option_data['maturity'] < maturity_upper_bound)]\n",
        "    amount_matrix_maturity[y,t]=len(options['market price'])\n",
        "\n",
        "for y in range(0,len(year_vec)):\n",
        "  for m in range(0,len(moneyness_vec)+1+len(maturity_vec)+1+1):\n",
        "    if (m<len(moneyness_vec)+1):\n",
        "      if (m==0):\n",
        "        print(str(year_vec[y]) + \" & \" + str(int(amount_matrix_moneyness[y,m])), end =\" \")\n",
        "      else:\n",
        "        print(\" & \" + str(int(amount_matrix_moneyness[y,m])), end =\" \")\n",
        "    else:\n",
        "      print(\" & \" + str(int(amount_matrix_maturity[y,m-(len(moneyness_vec)+1)])), end =\" \")\n",
        "  print(\"\\\\\" + \"\\\\\")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            " & Price & 58.52 & 27.26 &  67.75 & 40.51 &  75.86 & 42.0 &  65.4 & 36.43 \\\\\n",
            " & Observations & 1900 & &  2064 & &  920 & &  4677 &  \\\\\n",
            " & Price & 27.36 & 5.57 &  30.24 & 6.03 &  34.31 & 7.01 &  29.55 & 6.43 \\\\\n",
            " & Observations & 2892 & &  2804 & &  916 & &  6351 &  \\\\\n",
            " & Price & 13.62 & 4.88 &  17.67 & 5.71 &  21.44 & 6.71 &  16.65 & 6.25 \\\\\n",
            " & Observations & 6061 & &  6772 & &  2477 & &  14737 &  \\\\\n",
            " & Price & 5.72 & 3.83 &  10.47 & 5.17 &  14.43 & 6.24 &  9.51 & 5.93 \\\\\n",
            " & Observations & 6395 & &  8042 & &  3428 & &  17186 &  \\\\\n",
            " & Price & 2.79 & 2.9 &  6.31 & 4.41 &  9.75 & 5.49 &  5.65 & 4.87 \\\\\n",
            " & Observations & 5747 & &  7228 & &  2855 & &  15234 &  \\\\\n",
            " & Price & 1.42 & 1.92 &  2.91 & 3.0 &  4.49 & 3.99 &  2.82 & 3.19 \\\\\n",
            " & Observations & 13507 & &  23782 & &  10012 & &  45350 &  \\\\\n",
            " & Price & 9.44 & 15.41 &  10.72 & 16.61 &  13.42 & 18.62 &  10.78 & 16.59 \\\\\n",
            " & Observations & 36487 & &  50674 & &  20600 & &  103496 &  \\\\\n",
            "\n",
            "2003 & 1232  & 2873  & 6258  & 3160  & 4949  & 2254  & 10363 \\\\\n",
            "2004 & 615  & 3193  & 4845  & 2577  & 4185  & 1891  & 8653 \\\\\n",
            "2005 & 505  & 3301  & 4038  & 2403  & 3725  & 1716  & 7844 \\\\\n",
            "2006 & 364  & 3541  & 4274  & 2292  & 3948  & 1939  & 8179 \\\\\n",
            "2007 & 802  & 3873  & 6219  & 3368  & 5351  & 2175  & 10894 \\\\\n",
            "2008 & 2742  & 3191  & 7469  & 4541  & 6480  & 2381  & 13402 \\\\\n",
            "2009 & 1730  & 2507  & 8165  & 4034  & 6253  & 2115  & 12402 \\\\\n",
            "2010 & 1461  & 3009  & 7499  & 3955  & 6113  & 1901  & 11969 \\\\\n",
            "2011 & 1012  & 3138  & 6872  & 4200  & 5407  & 1415  & 11022 \\\\\n",
            "2012 & 562  & 3270  & 4936  & 3358  & 4263  & 1147  & 8768 \\\\\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eQJ7vWURYPyu"
      },
      "source": [
        "#Implied vol plot\n",
        "\n",
        "Some experimental plots with prices and implied volatility, didnt make the paper"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "f51ymZtDYSTN",
        "outputId": "85ef551e-cb5c-4f9d-ec8c-f51f53a938ac"
      },
      "source": [
        "#Obtain data for plotting\n",
        "#In this case I use options with a 30 day maturity, that are traded in the first month of 2003\n",
        "plot_data=option_data[(option_data['numerical_date']>20030000) & (option_data['numerical_date']<20030200) & (option_data['maturity']<31/250) & (option_data['maturity']>29/250) & (option_data['moneyness']>0) & (option_data['moneyness']<1.1)]\n",
        "maturity=plot_data['maturity'].to_numpy()\n",
        "interest_rate=plot_data['interest_rate'].to_numpy()/250\n",
        "strike=plot_data['strike_price'].to_numpy()\n",
        "underlying=plot_data['underlying'].to_numpy()\n",
        "implied_vol_given=plot_data['impl_volatility'].to_numpy()\n",
        "moneyness=plot_data['moneyness'].to_numpy()\n",
        "price=plot_data['market price'].to_numpy()\n",
        "\n",
        "#Only plot options that are not too deep\n",
        "ind=np.where((moneyness>0.96) & (moneyness<1.07))\n",
        "plt.figure(0)\n",
        "plt.plot(moneyness[ind],price[ind],\".k\", markersize=12)\n",
        "\n",
        "\n",
        "#THIS EXTENDS THE PLOT TO LOWER MONEYNESS\n",
        "#moneyness=np.hstack((moneyness,np.linspace(0.8,0.96,len(moneyness))))\n",
        "#strike=np.hstack((strike,strike))\n",
        "#underlying=np.multiply(moneyness,strike)\n",
        "#plot_data=pd.concat((plot_data,plot_data))\n",
        "#plot_data['underlying']=underlying\n",
        "#plot_data['strike_price']=strike\n",
        "##\n",
        "\n",
        "#Price with Heston model\n",
        "Heston = HestonModel(option_data_european,underlying_data)\n",
        "#model = AdHocBlackScholes(train)\n",
        "params=np.array([ 1.20106692e+00,  8.86737492e-02,  3.21321381e-01,  1.12821414e-03, -2.39050628e-01])\n",
        "params2 = np.array([0.489844, 0.140483, 4.734988, 0.069948, -0.147300])\n",
        "heston_prices=Heston.price_american_options(plot_data,params)\n",
        "heston_prices2=Heston.price_american_options(plot_data,params2)\n",
        "#AHBS_prices=model.price_AH_BS(plot_data)\n",
        "plt.plot(moneyness,heston_prices,marker='o',color='b')\n",
        "plt.plot(moneyness,heston_prices2,marker='o',color='g')\n",
        "plt.legend(['True option prices','Heston original params', 'Heston new params'])\n",
        "plt.ylabel('Option prices')\n",
        "plt.xlabel('Moneyness')\n",
        "\n",
        "##IMPLIED VOL CALCULATION\n",
        "N = norm.cdf\n",
        "\n",
        "def bs_put(S, K, T, r, vol):\n",
        "    '''\n",
        "    Calculates Black-Scholes put price\n",
        "    '''\n",
        "    d1 = (np.log(S/K) + (r + 0.5*vol**2)*T) / (vol*np.sqrt(T))\n",
        "    d2 = d1 - vol * np.sqrt(T)\n",
        "    return -S * norm.cdf(-d1) + np.exp(-r * T) * K * norm.cdf(-d2)\n",
        "\n",
        "def bs_vega(S, K, T, r, sigma):\n",
        "    '''\n",
        "    Calculates Black-Scholes vega\n",
        "    '''\n",
        "    d1 = (np.log(S / K) + (r + 0.5 * sigma ** 2) * T) / (sigma * np.sqrt(T))\n",
        "    return S * norm.pdf(d1) * np.sqrt(T)\n",
        "\n",
        "def find_vol(target_value, S, K, T, r, *args):\n",
        "    '''\n",
        "    Newton method for finding implied volatilty\n",
        "    '''\n",
        "    MAX_ITERATIONS = 2000\n",
        "    PRECISION = 1.0e-5\n",
        "    sigma = 0.5\n",
        "    for i in range(0, MAX_ITERATIONS):\n",
        "        price = bs_put(S, K, T, r, sigma)\n",
        "        vega = bs_vega(S, K, T, r, sigma)\n",
        "        diff = target_value - price  # our root\n",
        "        if (abs(diff) < PRECISION):\n",
        "            return sigma\n",
        "        sigma = sigma + diff/vega # f(x) / f'(x)\n",
        "    return sigma # value wasn't found, return best guess so far\n",
        "\n",
        "def implied_vol(underlying,strike,interest_rate,maturity,prices):\n",
        "    '''\n",
        "    Calculates implied volatility for given data\n",
        "    '''\n",
        "    implied_vol_vec=np.zeros(len(prices))\n",
        "    for i in range(0,len(prices)):\n",
        "      implied_vol_vec[i]=find_vol(prices[i],underlying[i],strike[i],maturity[i],interest_rate[i])\n",
        "    return implied_vol_vec\n",
        "\n",
        "def calculate_prices(underlying,strike,interest_rate,maturity,vol):\n",
        "    '''\n",
        "    Calculates Black-Scholes prices for given data\n",
        "    '''\n",
        "    prices_vec=np.zeros(len(vol))\n",
        "    for i in range(0,len(vol)):\n",
        "      prices_vec[i]=bs_put(underlying[i],strike[i],maturity[i],interest_rate[i],vol[i])\n",
        "    return prices_vec\n",
        "####\n",
        "\n",
        "#Calculate and plot implied volatilities\n",
        "implied_vol_market=implied_vol(underlying,strike,interest_rate,maturity,price) #*250/365\n",
        "implied_vol_heston=implied_vol(underlying,strike,interest_rate,maturity,heston_prices)\n",
        "#prices_vol = calculate_prices(underlying,strike,interest_rate,maturity,implied_vol_market)\n",
        "#plt.plot(moneyness[ind],prices_vol[ind],\".r\", markersize=12)\n",
        "\n",
        "plt.figure(1)\n",
        "plt.plot(moneyness[ind],implied_vol_market[ind],\".k\", markersize=12)\n",
        "plt.plot(moneyness[ind],implied_vol_given[ind],\".r\", markersize=12)\n",
        "plt.plot(moneyness,implied_vol_heston)\n",
        "plt.legend(['True implied volatility', 'Given implied volatility', 'AHBS'])\n",
        "plt.ylabel('Implied Volatilty')\n",
        "plt.xlabel('Moneyness')\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0\n",
            "1\n",
            "2\n",
            "3\n",
            "4\n",
            "5\n",
            "6\n",
            "7\n",
            "8\n",
            "9\n",
            "10\n",
            "11\n",
            "12\n",
            "13\n",
            "MAPE: 0.5427445003077614\n",
            "RMSE: 4.699854867265267\n",
            "total time: 0.7155412279980737, time per option: 0.05111008771414812\n",
            "0\n",
            "1\n",
            "2\n",
            "3\n",
            "4\n",
            "5\n",
            "6\n",
            "7\n",
            "8\n",
            "9\n",
            "10\n",
            "11\n",
            "12\n",
            "13\n",
            "MAPE: 0.461109173410865\n",
            "RMSE: 4.478219261225725\n",
            "total time: 0.8187739219983996, time per option: 0.058483851571314256\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 0, 'Moneyness')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 51
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2v784dKsk-xS"
      },
      "source": [
        "#Plots and tables results\n",
        "\n",
        "Creates the tables and figures for the results section\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MQZTmeislyht"
      },
      "source": [
        "##HELPER functoions\n",
        "def rmse(y_true,y_pred):\n",
        "  '''\n",
        "  Calculates RMSE\n",
        "  '''\n",
        "  return np.sqrt(np.mean(np.square(y_true-y_pred)))\n",
        "\n",
        "def mape(y_true,y_pred):\n",
        "  '''\n",
        "  Calculates MAPE\n",
        "  '''\n",
        "  return np.mean(np.divide(abs(y_true-y_pred),y_true))\n",
        "\n",
        "def print_table(labels,mape_mat,rmse_mat):\n",
        "  '''\n",
        "  Prints data in Latex table format\n",
        "  '''\n",
        "  rmse_mat=np.around(rmse_mat,4)\n",
        "  mape_mat=np.around(mape_mat,4)\n",
        "  for m in range(0,len(labels)):\n",
        "      print(labels[m] + \" & \", end = \"\")\n",
        "      for j in range(0,2):\n",
        "        for i in range(0,4):\n",
        "          if j==0:\n",
        "            if abs(decimal.Decimal(str(mape_mat[m,i])).as_tuple().exponent) < 4:\n",
        "              print(str(mape_mat[m,i]) + \"0 & \", end = \"\")\n",
        "            else:\n",
        "              print(str(mape_mat[m,i]) + \" & \", end = \"\")\n",
        "          else:\n",
        "            if i==3:\n",
        "              if abs(decimal.Decimal(str(rmse_mat[m,i])).as_tuple().exponent) < 4:\n",
        "                print(str(rmse_mat[m,i]) + \"0\", end = \"\")\n",
        "              else:\n",
        "                print(str(rmse_mat[m,i]), end =\" \")\n",
        "              print(\"\\\\\" + \"\\\\\")\n",
        "            else:\n",
        "              if abs(decimal.Decimal(str(rmse_mat[m,i])).as_tuple().exponent) < 4:\n",
        "                print(str(rmse_mat[m,i]) + \"0 & \", end = \"\")\n",
        "              else:\n",
        "                print(str(rmse_mat[m,i]) + \" & \", end = \"\")"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OcE-T89sl1jt"
      },
      "source": [
        "##DATA\n",
        "market_prices=option_data['market price']\n",
        "\n",
        "#Add the model estimated prices here\n",
        "ahbs_estimation = pd.read_csv('/content/drive/MyDrive/data aqf/estimation and prediction/ahbs_estimation.csv',header=None)\n",
        "ahbs_prediction = pd.read_csv('/content/drive/MyDrive/data aqf/estimation and prediction/ahbs_prediction.csv',header=None)\n",
        "heston_prediction = pd.read_csv('/content/drive/MyDrive/data aqf/estimation and prediction/heston_prediction.csv',header=None)\n",
        "heston_estimation=heston_prediction\n",
        "ann_estimation = pd.read_csv('/content/drive/MyDrive/data aqf/estimation and prediction/ANN_estimation.csv',header=None)\n",
        "ann_prediction = pd.read_csv('/content/drive/MyDrive/data aqf/estimation and prediction/ANN_prediction.csv',header=None,skip_blank_lines=False) ##Missing some zeros\n",
        "ann_prediction.columns=['temp']\n",
        "zeros = pd.DataFrame({'temp': np.zeros(31071)})\n",
        "ann_prediction=zeros.append(ann_prediction,ignore_index=True)\n",
        "bnn_estimation = pd.read_csv('/content/drive/MyDrive/data aqf/estimation and prediction/BNN_estimation.csv',header=None)\n",
        "bnn_prediction = pd.read_csv('/content/drive/MyDrive/data aqf/estimation and prediction/BNN_prediction.csv',header=None)\n",
        "gann_prediction = pd.read_csv('/content/drive/MyDrive/data aqf/estimation and prediction/gann_prediction.csv',header=None)\n",
        "gann_estimation = pd.read_csv('/content/drive/MyDrive/data aqf/estimation and prediction/gann_estimation.csv',header=None)\n",
        "gbnn_prediction = pd.read_csv('/content/drive/MyDrive/data aqf/estimation and prediction/gbnn_prediction_BETTER3.csv',header=None)\n",
        "gbnn_estimation = pd.read_csv('/content/drive/MyDrive/data aqf/estimation and prediction/gbnn_estimation_BETTER3.csv',header=None)\n",
        "svr_estimation = pd.read_csv('/content/drive/MyDrive/data aqf/estimation and prediction/svr_estimation.csv',header=None)\n",
        "svr_prediction = pd.read_csv('/content/drive/MyDrive/data aqf/estimation and prediction/svr_prediction.csv',header=None)\n",
        "\n",
        "##INPUTS\n",
        "estimated_prices=np.hstack((ahbs_estimation,heston_estimation,svr_estimation,ann_estimation,bnn_estimation,gann_estimation,gbnn_estimation)) #this should be a matrix, whose colums are estimated prices of models\n",
        "estimation_label=['AH-BS','Heston','SVR','BNN','FBNN','GBNN','GFBNN'] #labels correspoding to columns of the estimation matrix\n",
        "predicted_prices=np.hstack((ahbs_prediction,heston_prediction,svr_prediction,ann_prediction,bnn_prediction,gann_prediction,gbnn_prediction)) #this should be a matrix, whose colums are predicted prices of models\n",
        "prediction_label=['AH-BS','Heston','SVR','BNN','FBNN','GBNN','GFBNN'] #labels correspoding to columns of the prediction matrix\n",
        "\n",
        "only_plots=True\n",
        "if only_plots:\n",
        "  estimated_prices=np.hstack((ahbs_estimation,ann_estimation,bnn_estimation,gann_estimation,gbnn_estimation)) #this should be a matrix, whose colums are estimated prices of models\n",
        "  estimation_label=['AH-BS','BNN','FBNN','GBNN','GFBNN'] #labels correspoding to columns of the estimation matrix\n",
        "  predicted_prices=np.hstack((ahbs_prediction,ann_prediction,bnn_prediction,gann_prediction,gbnn_prediction)) #this should be a matrix, whose colums are predicted prices of models\n",
        "  prediction_label=['AH-BS','BNN','FBNN','GBNN','GFBNN'] #labels correspoding to columns of the prediction matrix\n",
        "\n",
        "estimation_models=len(estimation_label)\n",
        "prediction_models=len(prediction_label)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "BaEHbCPfl5BR",
        "outputId": "730596f6-6d9a-44e1-b0f0-a99af2e1eb9f"
      },
      "source": [
        "##TABLES\n",
        "#Create tables with estimation and prediction performance results\n",
        "rmse_mat_estimation=np.zeros([estimation_models,4])\n",
        "mape_mat_estimation=np.zeros([estimation_models,4])\n",
        "rmse_mat_prediction=np.zeros([prediction_models,4])\n",
        "mape_mat_prediction=np.zeros([prediction_models,4])\n",
        "moneyness=option_data['moneyness']\n",
        "dates=option_data['numerical_date']\n",
        "for k in range(0,2):\n",
        "  if k==0:\n",
        "    print(\"ESTIMATION\")\n",
        "    print()\n",
        "  if k==1:\n",
        "    print(\"PREDICTION\")\n",
        "    print()\n",
        "  for i in range(0,3):\n",
        "    for j in range(0,4):\n",
        "      if i==0:\n",
        "        year_lower_bound=2003\n",
        "        year_lower_bound_pred=2006\n",
        "        year_upper_bound=2007\n",
        "      if i==1:\n",
        "        year_lower_bound=2007\n",
        "        year_lower_bound_pred=2009\n",
        "        year_upper_bound=2010\n",
        "      if i==2:\n",
        "        year_lower_bound=2010\n",
        "        year_lower_bound_pred=2012\n",
        "        year_upper_bound=2013\n",
        "      if j==0:\n",
        "        moneyness_lower_bound=0\n",
        "        moneyness_upper_bound=0.97\n",
        "      if j==1:\n",
        "        moneyness_lower_bound=0.97\n",
        "        moneyness_upper_bound=1.03\n",
        "      if j==2:\n",
        "        moneyness_lower_bound=1.03\n",
        "        moneyness_upper_bound=10**4\n",
        "      if j==3:\n",
        "        moneyness_lower_bound=0\n",
        "        moneyness_upper_bound=10**4\n",
        "      if k==0:\n",
        "        for m in range(0,estimation_models):\n",
        "          ind=np.where((moneyness>=moneyness_lower_bound) & (moneyness<moneyness_upper_bound) & (dates>=year_lower_bound*10**4) & (dates<=year_upper_bound*10**4))\n",
        "          rmse_mat_estimation[m,j]=rmse(market_prices.to_numpy()[ind],estimated_prices[ind,m])\n",
        "          mape_mat_estimation[m,j]=mape(market_prices.to_numpy()[ind],estimated_prices[ind,m])\n",
        "      if k==1:\n",
        "        for m in range(0,prediction_models):\n",
        "          ind=np.where((moneyness>=moneyness_lower_bound) & (moneyness<moneyness_upper_bound) & (dates>=year_lower_bound_pred*10**4 + 701) & (dates<=year_upper_bound*10**4))\n",
        "          rmse_mat_prediction[m,j]=rmse(market_prices.to_numpy()[ind],predicted_prices[ind,m])\n",
        "          mape_mat_prediction[m,j]=mape(market_prices.to_numpy()[ind],predicted_prices[ind,m])\n",
        "    if k==0:\n",
        "      print_table(estimation_label,mape_mat_estimation,rmse_mat_estimation)\n",
        "      print()\n",
        "    if k==1:\n",
        "      print_table(prediction_label,mape_mat_prediction,rmse_mat_prediction)\n",
        "      print()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "ESTIMATION\n",
            "\n",
            "AH-BS & 0.1447 & 0.6555 & 0.9240 & 0.7647 & 7.6435 & 5.0746 & 2.6993 & 4.2488 \\\\\n",
            "Heston & 0.2756 & 0.5703 & 0.9052 & 0.7330 & 8.5406 & 6.2061 & 2.7970 & 4.9171 \\\\\n",
            "BNN & 0.0511 & 0.2411 & 0.6254 & 0.4393 & 2.4808 & 2.5411 & 1.7402 & 2.1293 \\\\\n",
            "FBNN & 0.1079 & 0.2940 & 0.8671 & 0.5971 & 4.8716 & 2.7166 & 1.9232 & 2.5705 \\\\\n",
            "GBNN & 0.0971 & 0.2016 & 1.0822 & 0.6814 & 7.4975 & 2.8739 & 2.3369 & 3.2289 \\\\\n",
            "GFBNN & 0.1557 & 0.2161 & 1.1083 & 0.7058 & 7.3294 & 2.8151 & 2.2431 & 3.1419 \\\\\n",
            "SVR & 0.0248 & 0.1880 & 0.3911 & 0.2879 & 1.3186 & 2.4598 & 1.6240 & 1.9558 \\\\\n",
            "\n",
            "AH-BS & 0.2317 & 0.4717 & 0.9425 & 0.7176 & 18.8310 & 7.1930 & 4.6597 & 8.7969 \\\\\n",
            "Heston & 0.1472 & 0.3726 & 0.9665 & 0.6939 & 7.2224 & 6.9228 & 6.1995 & 6.5485 \\\\\n",
            "BNN & 0.1191 & 0.3016 & 0.7782 & 0.5592 & 9.4651 & 6.0387 & 4.1301 & 5.7046 \\\\\n",
            "FBNN & 0.1278 & 0.3296 & 0.9692 & 0.6815 & 11.0497 & 5.5933 & 4.6731 & 6.2217 \\\\\n",
            "GBNN & 0.1644 & 0.3332 & 0.6190 & 0.4791 & 11.2890 & 6.6794 & 4.1815 & 6.3532 \\\\\n",
            "GFBNN & 0.1411 & 0.3201 & 0.7699 & 0.5622 & 18.0693 & 6.2487 & 4.5214 & 8.3234 \\\\\n",
            "SVR & 0.0760 & 0.2858 & 0.5666 & 0.4229 & 5.3421 & 4.9628 & 3.4916 & 4.2172 \\\\\n",
            "\n",
            "AH-BS & 0.1492 & 0.6351 & 1.0059 & 0.8141 & 8.9260 & 7.0103 & 3.7282 & 5.5349 \\\\\n",
            "Heston & 0.3054 & 0.4287 & 0.9586 & 0.7390 & 11.3282 & 6.5980 & 4.3161 & 6.0413 \\\\\n",
            "BNN & 0.0697 & 0.1783 & 0.5956 & 0.4216 & 3.8853 & 3.1521 & 2.2547 & 2.7348 \\\\\n",
            "FBNN & 0.1034 & 0.2453 & 0.7326 & 0.5280 & 5.9372 & 3.9959 & 2.8588 & 3.6155 \\\\\n",
            "GBNN & 0.1348 & 0.3250 & 0.4835 & 0.4032 & 7.9738 & 3.4380 & 2.2457 & 3.5562 \\\\\n",
            "GFBNN & 0.0777 & 0.2597 & 0.8690 & 0.6127 & 4.6587 & 3.0891 & 3.0632 & 3.2570\\\\\n",
            "SVR & 0.0367 & 0.1413 & 0.3279 & 0.2448 & 2.0875 & 2.7903 & 1.9907 & 2.2659 \\\\\n",
            "\n",
            "PREDICTION\n",
            "\n",
            "AH-BS & 0.4568 & 0.5986 & 0.9566 & 0.7794 & 14.9483 & 5.8512 & 1.9043 & 4.9307 \\\\\n",
            "Heston & 0.3661 & 0.7687 & 0.8478 & 0.7970 & 10.1597 & 7.1658 & 1.4042 & 5.2367 \\\\\n",
            "BNN & 0.0731 & 0.4951 & 1.3938 & 0.9469 & 3.3234 & 3.0895 & 1.8584 & 2.5378 \\\\\n",
            "FBNN & 0.1119 & 0.4824 & 0.7334 & 0.6006 & 4.7709 & 2.3778 & 1.3955 & 2.0666 \\\\\n",
            "GBNN & 0.0685 & 0.1163 & 0.5580 & 0.3434 & 2.7866 & 0.9163 & 0.6759 & 0.9263 \\\\\n",
            "GFBNN & 0.1972 & 0.2025 & 1.4088 & 0.8265 & 7.6823 & 1.1723 & 0.9404 & 1.7094 \\\\\n",
            "SVR & 0.1063 & 0.3372 & 1.2899 & 0.8229 & 8.2536 & 2.6560 & 2.0790 & 2.7476 \\\\\n",
            "\n",
            "AH-BS & 0.3731 & 1.5464 & 2.8732 & 2.3269 & 23.0709 & 17.4340 & 9.7628 & 13.6181 \\\\\n",
            "Heston & 0.2723 & 0.2872 & 0.9716 & 0.7468 & 10.2869 & 4.3127 & 3.7058 & 4.8731 \\\\\n",
            "BNN & 0.1947 & 0.1407 & 0.9540 & 0.6938 & 16.0931 & 2.3304 & 1.5409 & 5.2790\\\\\n",
            "FBNN & 0.1605 & 0.1436 & 2.6347 & 1.8234 & 18.0752 & 2.0156 & 2.4466 & 6.0440\\\\\n",
            "GBNN & 0.1357 & 0.0763 & 0.3440 & 0.2624 & 22.8218 & 1.1836 & 0.6757 & 7.1378 \\\\\n",
            "GFBNN & 0.1835 & 0.1229 & 0.7535 & 0.5536 & 32.9438 & 1.6707 & 1.1076 & 10.3111 \\\\\n",
            "SVR & 0.2667 & 0.2340 & 3.7183 & 2.5844 & 57.0133 & 3.6286 & 5.4609 & 18.3617 \\\\\n",
            "\n",
            "AH-BS & 0.5130 & 0.6090 & 0.9733 & 0.7961 & 22.0771 & 7.6157 & 3.3892 & 7.5637 \\\\\n",
            "Heston & 0.4369 & 0.5473 & 0.9240 & 0.7402 & 15.3959 & 7.7987 & 2.7082 & 6.5056 \\\\\n",
            "BNN & 0.1607 & 0.1352 & 0.7288 & 0.4503 & 7.2774 & 1.6411 & 1.1310 & 2.1750\\\\\n",
            "FBNN & 0.2536 & 0.2858 & 0.8392 & 0.5764 & 10.5218 & 2.7273 & 1.1853 & 3.1576 \\\\\n",
            "GBNN & 0.0938 & 0.1031 & 0.3731 & 0.2452 & 6.0479 & 1.0399 & 0.7662 & 1.6692 \\\\\n",
            "GFBNN & 0.0408 & 0.1778 & 0.7253 & 0.4595 & 4.0219 & 1.3117 & 1.3433 & 1.6018 \\\\\n",
            "SVR & 0.1627 & 0.1887 & 0.9917 & 0.6115 & 16.7541 & 2.2380 & 2.6353 & 4.6154 \\\\\n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "klEUDGIYlCGK",
        "outputId": "f1f29af4-b878-4838-a54b-d7340ee69dbc"
      },
      "source": [
        "##FIGURES\n",
        "#Create Figure 4 from the paper, which plots RMSE against years\n",
        "years=10\n",
        "year_vec=np.linspace(2003,2012,years)\n",
        "rmse_mat=np.zeros([years,estimation_models])\n",
        "option_data.reset_index()\n",
        "dates=option_data['numerical_date']\n",
        "for m in range(0,estimation_models):\n",
        "  for y in range(0,years):\n",
        "    year=year_vec[y]\n",
        "    ind=np.where((dates>year*10**4) & (dates<(year+1)*10**4))\n",
        "    rmse_mat[y,m]=rmse(market_prices.to_numpy()[ind],estimated_prices[ind,m])\n",
        "\n",
        "plt.figure(0)\n",
        "marker = itertools.cycle(('o', '^', 's', 'P', '*','d', 'H')) \n",
        "linestyles = itertools.cycle(('solid', 'dotted', 'dashed'))\n",
        "for m in range(0,estimation_models):\n",
        "  #plt.plot(year_vec,rmse_mat[:,m])\n",
        "  plt.plot(year_vec,rmse_mat[:,m],marker=next(marker),linestyle = next(linestyles))\n",
        "plt.legend(estimation_label)\n",
        "plt.ylabel('Root Mean Squared Error (RMSE)')\n",
        "plt.xlabel('Year')\n",
        "plt.xticks(year_vec)\n",
        "plt.savefig(\"RMSEyear.eps\")\n",
        "files.download(\"RMSEyear.eps\") \n",
        "\n",
        "#Create Figure 5 from the paper, which plots RMSE and MAPE against years\n",
        "prediction=True\n",
        "\n",
        "for t in range(0,3):\n",
        "  dots=5\n",
        "  moneyness=option_data['moneyness']\n",
        "  maturity=option_data['maturity']*250\n",
        "  dates=option_data['numerical_date']\n",
        "  moneyness_vec=np.linspace(0.95,1.09,dots+1)\n",
        "  plot_vec=np.ones(dots)\n",
        "  rmse_mat=np.zeros([dots,estimation_models])\n",
        "  mape_mat=np.zeros([dots,estimation_models])\n",
        "  for m in range(0,estimation_models):\n",
        "    for d in range(0,dots):\n",
        "        if t==0:\n",
        "          ind=np.where((moneyness>=moneyness_vec[d]) & (moneyness<=moneyness_vec[d+1]) & (maturity<30))\n",
        "          if prediction:\n",
        "            ind=np.where((moneyness>=moneyness_vec[d]) & (moneyness<=moneyness_vec[d+1]) & (maturity<30) & (((dates>=20060700) & (dates<20070000)) | ((dates>=20090700) & (dates<20100000)) | ((dates>=20120700) & (dates<20130000))))\n",
        "        if t==1:\n",
        "          ind=np.where((moneyness>=moneyness_vec[d]) & (moneyness<=moneyness_vec[d+1]) & (maturity>=30) & (maturity<=60))\n",
        "          if prediction:\n",
        "            ind=np.where((moneyness>=moneyness_vec[d]) & (moneyness<=moneyness_vec[d+1]) & (maturity>=30) & (maturity<=60) & (((dates>=20060700) & (dates<20070000)) | ((dates>=20090700) & (dates<20100000)) | ((dates>=20120700) & (dates<20130000))))\n",
        "        if t==2:\n",
        "          ind=np.where((moneyness>=moneyness_vec[d]) & (moneyness<=moneyness_vec[d+1]) & (maturity>60))\n",
        "          if prediction:\n",
        "            ind=np.where((moneyness>=moneyness_vec[d]) & (moneyness<=moneyness_vec[d+1]) & (maturity>60) & (((dates>=20060700) & (dates<20070000)) | ((dates>=20090700) & (dates<20100000)) | ((dates>=20120700) & (dates<20130000))))\n",
        "        if prediction:\n",
        "          rmse_mat[d,m]=rmse(market_prices.to_numpy()[ind],predicted_prices[ind,m])\n",
        "          mape_mat[d,m]=mape(market_prices.to_numpy()[ind],predicted_prices[ind,m])\n",
        "        else:\n",
        "          rmse_mat[d,m]=rmse(market_prices.to_numpy()[ind],estimated_prices[ind,m])\n",
        "          mape_mat[d,m]=mape(market_prices.to_numpy()[ind],estimated_prices[ind,m])\n",
        "        plot_vec[d]=moneyness_vec[d]/2+moneyness_vec[d+1]/2\n",
        "\n",
        "  if t==0:\n",
        "    maturity_label=\"Maturity: <30 days\"\n",
        "    plot_title=\"Maturity30.eps\"\n",
        "  if t==1:\n",
        "    maturity_label=\"Maturity: 30-60 days\"\n",
        "    plot_title=\"Maturity3060.eps\"\n",
        "  if t==2:\n",
        "    maturity_label=\"Maturity: >60 days\"\n",
        "    plot_title=\"Maturity60.eps\"\n",
        "  plt.figure(1+t*2)\n",
        "  marker = itertools.cycle(('o', '^', 's', 'P', '*','d', 'H')) \n",
        "  linestyles = itertools.cycle(('solid', 'dotted', 'dashed'))\n",
        "  for m in range(0,estimation_models):\n",
        "    #plt.plot(plot_vec,rmse_mat[:,m],marker='o')\n",
        "    plt.plot(plot_vec,rmse_mat[:,m],marker=next(marker),linestyle = next(linestyles))\n",
        "  #plt.legend(estimation_label)\n",
        "  plt.ylabel('Root Mean Squared Error (RMSE)')\n",
        "  plt.xlabel('Moneyness')\n",
        "  ax2 = plt.twiny()\n",
        "  ax2.set_xlabel(maturity_label)\n",
        "  ax2.tick_params(axis='x', which='both', bottom=False, top=False, labelbottom=False, labeltop=False) \n",
        "  plt.savefig(\"RMSE\" + plot_title)\n",
        "  files.download(\"RMSE\" + plot_title)\n",
        "\n",
        "  plt.figure(2+t*2)\n",
        "  marker = itertools.cycle(('o', '^', 's', 'P', '*','d', 'H')) \n",
        "  linestyles = itertools.cycle(('solid', 'dotted', 'dashed'))\n",
        "  for m in range(0,estimation_models):\n",
        "    #plt.plot(plot_vec,mape_mat[:,m],marker='o')\n",
        "    plt.plot(plot_vec,mape_mat[:,m],marker=next(marker),linestyle = next(linestyles))\n",
        "  if t==0:\n",
        "    plt.legend(estimation_label)\n",
        "  plt.ylabel('Mean Absolute Percentage Error (MAPE)')\n",
        "  plt.xlabel('Moneyness')\n",
        "  ax2 = plt.twiny()\n",
        "  ax2.set_xlabel(maturity_label)\n",
        "  ax2.tick_params(axis='x', which='both', bottom=False, top=False, labelbottom=False, labeltop=False) \n",
        "  plt.savefig(\"MAPE\" + plot_title)\n",
        "  files.download(\"MAPE\" + plot_title)\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.\n",
            "The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "application/javascript": [
              "\n",
              "    async function download(id, filename, size) {\n",
              "      if (!google.colab.kernel.accessAllowed) {\n",
              "        return;\n",
              "      }\n",
              "      const div = document.createElement('div');\n",
              "      const label = document.createElement('label');\n",
              "      label.textContent = `Downloading \"${filename}\": `;\n",
              "      div.appendChild(label);\n",
              "      const progress = document.createElement('progress');\n",
              "      progress.max = size;\n",
              "      div.appendChild(progress);\n",
              "      document.body.appendChild(div);\n",
              "\n",
              "      const buffers = [];\n",
              "      let downloaded = 0;\n",
              "\n",
              "      const channel = await google.colab.kernel.comms.open(id);\n",
              "      // Send a message to notify the kernel that we're ready.\n",
              "      channel.send({})\n",
              "\n",
              "      for await (const message of channel.messages) {\n",
              "        // Send a message to notify the kernel that we're ready.\n",
              "        channel.send({})\n",
              "        if (message.buffers) {\n",
              "          for (const buffer of message.buffers) {\n",
              "            buffers.push(buffer);\n",
              "            downloaded += buffer.byteLength;\n",
              "            progress.value = downloaded;\n",
              "          }\n",
              "        }\n",
              "      }\n",
              "      const blob = new Blob(buffers, {type: 'application/binary'});\n",
              "      const a = document.createElement('a');\n",
              "      a.href = window.URL.createObjectURL(blob);\n",
              "      a.download = filename;\n",
              "      div.appendChild(a);\n",
              "      a.click();\n",
              "      div.remove();\n",
              "    }\n",
              "  "
            ],
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "application/javascript": [
              "download(\"download_6f33e667-c1a5-44d1-bc1f-0f557c79e1e6\", \"RMSEyear.eps\", 30344)"
            ],
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "application/javascript": [
              "\n",
              "    async function download(id, filename, size) {\n",
              "      if (!google.colab.kernel.accessAllowed) {\n",
              "        return;\n",
              "      }\n",
              "      const div = document.createElement('div');\n",
              "      const label = document.createElement('label');\n",
              "      label.textContent = `Downloading \"${filename}\": `;\n",
              "      div.appendChild(label);\n",
              "      const progress = document.createElement('progress');\n",
              "      progress.max = size;\n",
              "      div.appendChild(progress);\n",
              "      document.body.appendChild(div);\n",
              "\n",
              "      const buffers = [];\n",
              "      let downloaded = 0;\n",
              "\n",
              "      const channel = await google.colab.kernel.comms.open(id);\n",
              "      // Send a message to notify the kernel that we're ready.\n",
              "      channel.send({})\n",
              "\n",
              "      for await (const message of channel.messages) {\n",
              "        // Send a message to notify the kernel that we're ready.\n",
              "        channel.send({})\n",
              "        if (message.buffers) {\n",
              "          for (const buffer of message.buffers) {\n",
              "            buffers.push(buffer);\n",
              "            downloaded += buffer.byteLength;\n",
              "            progress.value = downloaded;\n",
              "          }\n",
              "        }\n",
              "      }\n",
              "      const blob = new Blob(buffers, {type: 'application/binary'});\n",
              "      const a = document.createElement('a');\n",
              "      a.href = window.URL.createObjectURL(blob);\n",
              "      a.download = filename;\n",
              "      div.appendChild(a);\n",
              "      a.click();\n",
              "      div.remove();\n",
              "    }\n",
              "  "
            ],
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "application/javascript": [
              "download(\"download_c62d4628-d8d8-42f2-974b-77bdc89409e2\", \"RMSEMaturity30.eps\", 24551)"
            ],
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.\n",
            "The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "application/javascript": [
              "\n",
              "    async function download(id, filename, size) {\n",
              "      if (!google.colab.kernel.accessAllowed) {\n",
              "        return;\n",
              "      }\n",
              "      const div = document.createElement('div');\n",
              "      const label = document.createElement('label');\n",
              "      label.textContent = `Downloading \"${filename}\": `;\n",
              "      div.appendChild(label);\n",
              "      const progress = document.createElement('progress');\n",
              "      progress.max = size;\n",
              "      div.appendChild(progress);\n",
              "      document.body.appendChild(div);\n",
              "\n",
              "      const buffers = [];\n",
              "      let downloaded = 0;\n",
              "\n",
              "      const channel = await google.colab.kernel.comms.open(id);\n",
              "      // Send a message to notify the kernel that we're ready.\n",
              "      channel.send({})\n",
              "\n",
              "      for await (const message of channel.messages) {\n",
              "        // Send a message to notify the kernel that we're ready.\n",
              "        channel.send({})\n",
              "        if (message.buffers) {\n",
              "          for (const buffer of message.buffers) {\n",
              "            buffers.push(buffer);\n",
              "            downloaded += buffer.byteLength;\n",
              "            progress.value = downloaded;\n",
              "          }\n",
              "        }\n",
              "      }\n",
              "      const blob = new Blob(buffers, {type: 'application/binary'});\n",
              "      const a = document.createElement('a');\n",
              "      a.href = window.URL.createObjectURL(blob);\n",
              "      a.download = filename;\n",
              "      div.appendChild(a);\n",
              "      a.click();\n",
              "      div.remove();\n",
              "    }\n",
              "  "
            ],
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "application/javascript": [
              "download(\"download_32fcde6d-81d4-4635-bab5-0c9a4171e8b6\", \"MAPEMaturity30.eps\", 32579)"
            ],
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "application/javascript": [
              "\n",
              "    async function download(id, filename, size) {\n",
              "      if (!google.colab.kernel.accessAllowed) {\n",
              "        return;\n",
              "      }\n",
              "      const div = document.createElement('div');\n",
              "      const label = document.createElement('label');\n",
              "      label.textContent = `Downloading \"${filename}\": `;\n",
              "      div.appendChild(label);\n",
              "      const progress = document.createElement('progress');\n",
              "      progress.max = size;\n",
              "      div.appendChild(progress);\n",
              "      document.body.appendChild(div);\n",
              "\n",
              "      const buffers = [];\n",
              "      let downloaded = 0;\n",
              "\n",
              "      const channel = await google.colab.kernel.comms.open(id);\n",
              "      // Send a message to notify the kernel that we're ready.\n",
              "      channel.send({})\n",
              "\n",
              "      for await (const message of channel.messages) {\n",
              "        // Send a message to notify the kernel that we're ready.\n",
              "        channel.send({})\n",
              "        if (message.buffers) {\n",
              "          for (const buffer of message.buffers) {\n",
              "            buffers.push(buffer);\n",
              "            downloaded += buffer.byteLength;\n",
              "            progress.value = downloaded;\n",
              "          }\n",
              "        }\n",
              "      }\n",
              "      const blob = new Blob(buffers, {type: 'application/binary'});\n",
              "      const a = document.createElement('a');\n",
              "      a.href = window.URL.createObjectURL(blob);\n",
              "      a.download = filename;\n",
              "      div.appendChild(a);\n",
              "      a.click();\n",
              "      div.remove();\n",
              "    }\n",
              "  "
            ],
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "application/javascript": [
              "download(\"download_7737d65e-0a6b-48cc-a966-02e892f35070\", \"RMSEMaturity3060.eps\", 24612)"
            ],
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "application/javascript": [
              "\n",
              "    async function download(id, filename, size) {\n",
              "      if (!google.colab.kernel.accessAllowed) {\n",
              "        return;\n",
              "      }\n",
              "      const div = document.createElement('div');\n",
              "      const label = document.createElement('label');\n",
              "      label.textContent = `Downloading \"${filename}\": `;\n",
              "      div.appendChild(label);\n",
              "      const progress = document.createElement('progress');\n",
              "      progress.max = size;\n",
              "      div.appendChild(progress);\n",
              "      document.body.appendChild(div);\n",
              "\n",
              "      const buffers = [];\n",
              "      let downloaded = 0;\n",
              "\n",
              "      const channel = await google.colab.kernel.comms.open(id);\n",
              "      // Send a message to notify the kernel that we're ready.\n",
              "      channel.send({})\n",
              "\n",
              "      for await (const message of channel.messages) {\n",
              "        // Send a message to notify the kernel that we're ready.\n",
              "        channel.send({})\n",
              "        if (message.buffers) {\n",
              "          for (const buffer of message.buffers) {\n",
              "            buffers.push(buffer);\n",
              "            downloaded += buffer.byteLength;\n",
              "            progress.value = downloaded;\n",
              "          }\n",
              "        }\n",
              "      }\n",
              "      const blob = new Blob(buffers, {type: 'application/binary'});\n",
              "      const a = document.createElement('a');\n",
              "      a.href = window.URL.createObjectURL(blob);\n",
              "      a.download = filename;\n",
              "      div.appendChild(a);\n",
              "      a.click();\n",
              "      div.remove();\n",
              "    }\n",
              "  "
            ],
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "application/javascript": [
              "download(\"download_589b9ba6-0cd7-4329-bdce-4e066f2bb3be\", \"MAPEMaturity3060.eps\", 27009)"
            ],
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "application/javascript": [
              "\n",
              "    async function download(id, filename, size) {\n",
              "      if (!google.colab.kernel.accessAllowed) {\n",
              "        return;\n",
              "      }\n",
              "      const div = document.createElement('div');\n",
              "      const label = document.createElement('label');\n",
              "      label.textContent = `Downloading \"${filename}\": `;\n",
              "      div.appendChild(label);\n",
              "      const progress = document.createElement('progress');\n",
              "      progress.max = size;\n",
              "      div.appendChild(progress);\n",
              "      document.body.appendChild(div);\n",
              "\n",
              "      const buffers = [];\n",
              "      let downloaded = 0;\n",
              "\n",
              "      const channel = await google.colab.kernel.comms.open(id);\n",
              "      // Send a message to notify the kernel that we're ready.\n",
              "      channel.send({})\n",
              "\n",
              "      for await (const message of channel.messages) {\n",
              "        // Send a message to notify the kernel that we're ready.\n",
              "        channel.send({})\n",
              "        if (message.buffers) {\n",
              "          for (const buffer of message.buffers) {\n",
              "            buffers.push(buffer);\n",
              "            downloaded += buffer.byteLength;\n",
              "            progress.value = downloaded;\n",
              "          }\n",
              "        }\n",
              "      }\n",
              "      const blob = new Blob(buffers, {type: 'application/binary'});\n",
              "      const a = document.createElement('a');\n",
              "      a.href = window.URL.createObjectURL(blob);\n",
              "      a.download = filename;\n",
              "      div.appendChild(a);\n",
              "      a.click();\n",
              "      div.remove();\n",
              "    }\n",
              "  "
            ],
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "application/javascript": [
              "download(\"download_c0f042d7-6116-4f18-ba5a-7ad1aae73f7c\", \"RMSEMaturity60.eps\", 24133)"
            ],
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "application/javascript": [
              "\n",
              "    async function download(id, filename, size) {\n",
              "      if (!google.colab.kernel.accessAllowed) {\n",
              "        return;\n",
              "      }\n",
              "      const div = document.createElement('div');\n",
              "      const label = document.createElement('label');\n",
              "      label.textContent = `Downloading \"${filename}\": `;\n",
              "      div.appendChild(label);\n",
              "      const progress = document.createElement('progress');\n",
              "      progress.max = size;\n",
              "      div.appendChild(progress);\n",
              "      document.body.appendChild(div);\n",
              "\n",
              "      const buffers = [];\n",
              "      let downloaded = 0;\n",
              "\n",
              "      const channel = await google.colab.kernel.comms.open(id);\n",
              "      // Send a message to notify the kernel that we're ready.\n",
              "      channel.send({})\n",
              "\n",
              "      for await (const message of channel.messages) {\n",
              "        // Send a message to notify the kernel that we're ready.\n",
              "        channel.send({})\n",
              "        if (message.buffers) {\n",
              "          for (const buffer of message.buffers) {\n",
              "            buffers.push(buffer);\n",
              "            downloaded += buffer.byteLength;\n",
              "            progress.value = downloaded;\n",
              "          }\n",
              "        }\n",
              "      }\n",
              "      const blob = new Blob(buffers, {type: 'application/binary'});\n",
              "      const a = document.createElement('a');\n",
              "      a.href = window.URL.createObjectURL(blob);\n",
              "      a.download = filename;\n",
              "      div.appendChild(a);\n",
              "      a.click();\n",
              "      div.remove();\n",
              "    }\n",
              "  "
            ],
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "application/javascript": [
              "download(\"download_a3d4c9ec-4b25-4ad6-a314-13abf17cc6b4\", \"MAPEMaturity60.eps\", 25000)"
            ],
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 315
        },
        "id": "rqJ70v1PMAjn",
        "outputId": "74ee577d-7768-4ce6-9188-bfb6a17b7297"
      },
      "source": [
        "#Create Figure 3 from the paper, which plots options traded on certain days\n",
        "moneyness=option_data['moneyness']\n",
        "maturity=option_data['maturity']*250\n",
        "dates=option_data['numerical_date']\n",
        "prices=option_data['market price']\n",
        "plot_ind=np.where((moneyness>0) & (moneyness<1.1) & (maturity>29) & (maturity<31) & (dates>=20040000) & (dates<20040200))\n",
        "plt.figure(0)\n",
        "marker = itertools.cycle(('o', '^', 's', 'P', '*','d', 'H')) \n",
        "linestyles = itertools.cycle(('solid', 'dotted', 'dashed'))\n",
        "moneyness_plot=moneyness.to_numpy()[plot_ind]\n",
        "prices_plot=prices.to_numpy()[plot_ind]\n",
        "plt.plot(moneyness_plot,prices_plot,\".k\", markersize=12)\n",
        "for m in range(0,estimation_models):\n",
        "  if not only_plots:\n",
        "    if m>0 and m<3:\n",
        "      if m==1:\n",
        "        plt.plot(moneyness_plot,estimated_prices[plot_ind,m].T,color='cadetblue',linestyle = 'dashdot')\n",
        "      if m==2:\n",
        "        plt.plot(moneyness_plot,estimated_prices[plot_ind,m].T,color='magenta',linestyle = 'dashdot')\n",
        "    else:\n",
        "      plt.plot(moneyness_plot,estimated_prices[plot_ind,m].T,linestyle = next(linestyles))\n",
        "  else:\n",
        "    plt.plot(moneyness_plot,estimated_prices[plot_ind,m].T,linestyle = next(linestyles))\n",
        "labels=estimation_label.copy()\n",
        "labels.insert(0,'True price')\n",
        "plt.legend(labels)\n",
        "plt.ylabel('Option prices')\n",
        "plt.xlabel('Moneyness')\n",
        "plt.savefig(\"figure3paper.eps\")\n",
        "files.download(\"figure3paper.eps\")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.\n",
            "The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "application/javascript": [
              "\n",
              "    async function download(id, filename, size) {\n",
              "      if (!google.colab.kernel.accessAllowed) {\n",
              "        return;\n",
              "      }\n",
              "      const div = document.createElement('div');\n",
              "      const label = document.createElement('label');\n",
              "      label.textContent = `Downloading \"${filename}\": `;\n",
              "      div.appendChild(label);\n",
              "      const progress = document.createElement('progress');\n",
              "      progress.max = size;\n",
              "      div.appendChild(progress);\n",
              "      document.body.appendChild(div);\n",
              "\n",
              "      const buffers = [];\n",
              "      let downloaded = 0;\n",
              "\n",
              "      const channel = await google.colab.kernel.comms.open(id);\n",
              "      // Send a message to notify the kernel that we're ready.\n",
              "      channel.send({})\n",
              "\n",
              "      for await (const message of channel.messages) {\n",
              "        // Send a message to notify the kernel that we're ready.\n",
              "        channel.send({})\n",
              "        if (message.buffers) {\n",
              "          for (const buffer of message.buffers) {\n",
              "            buffers.push(buffer);\n",
              "            downloaded += buffer.byteLength;\n",
              "            progress.value = downloaded;\n",
              "          }\n",
              "        }\n",
              "      }\n",
              "      const blob = new Blob(buffers, {type: 'application/binary'});\n",
              "      const a = document.createElement('a');\n",
              "      a.href = window.URL.createObjectURL(blob);\n",
              "      a.download = filename;\n",
              "      div.appendChild(a);\n",
              "      a.click();\n",
              "      div.remove();\n",
              "    }\n",
              "  "
            ],
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "application/javascript": [
              "download(\"download_b36c1503-ab56-4167-b7f7-070c4f111b9f\", \"figure3paper.eps\", 28186)"
            ],
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sIdQL_IWt0Pu"
      },
      "source": [
        "#support vector regression (SVR)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "_eDhsrwut7QI",
        "outputId": "94724afb-35da-4ac4-d7c1-949603ffea81"
      },
      "source": [
        "#This array will have all prices obtained from the\n",
        "predicted_prices_all=[]\n",
        "predicted_prices_in_and_out=[]\n",
        "\n",
        "for i in range(0,3):\n",
        "  if i==0:\n",
        "    period='pre-crisis'\n",
        "  if i==1:\n",
        "    period='crisis'\n",
        "  if i==2:\n",
        "    period='post-crisis'\n",
        "  if period == 'pre-crisis':\n",
        "    train = option_data[(option_data['date'] >= pd.Timestamp(2003,1,1)) & (option_data['date'] < pd.Timestamp(2006,7,1))]\n",
        "    test = option_data[(option_data['date'] >= pd.Timestamp(2006,7,1)) & (option_data['date'] < pd.Timestamp(2007,1,1))]\n",
        "  elif period == 'crisis':\n",
        "    train = option_data[(option_data['date'] >= pd.Timestamp(2007,1,1)) & (option_data['date'] < pd.Timestamp(2009,7,1))]\n",
        "    test = option_data[(option_data['date'] >= pd.Timestamp(2009,7,1)) & (option_data['date'] < pd.Timestamp(2010,1,1))]\n",
        "  elif period == 'post-crisis':\n",
        "    train = option_data[(option_data['date'] >= pd.Timestamp(2010,1,1)) & (option_data['date'] < pd.Timestamp(2012,7,1))]\n",
        "    test = option_data[(option_data['date'] >= pd.Timestamp(2012,7,1)) & (option_data['date'] < pd.Timestamp(2013,1,1))]\n",
        "  else:\n",
        "    raise ValueError('Not a valid string for period')\n",
        "\n",
        "  #Estimate SVR and estimate in sample\n",
        "  X = train[['moneyness','maturity']].values\n",
        "  print(np.shape(X)[0])\n",
        "  X_offset = X.min(0)  # or X.mean(0)\n",
        "  X_scale = X.max(0) - X_offset  # or X.std(0)\n",
        "  X_scaled = np.asarray((X - X_offset) / X_scale).astype('float32')\n",
        "  y = train[['market price']].values.ravel()\n",
        "  y_offset = y.min(0)  # or X.mean(0)\n",
        "  y_scale = y.max(0) - y_offset  # or X.std(0)\n",
        "  y_scaled = np.asarray((y - y_offset) / y_scale).astype('float32')\n",
        "  C=1\n",
        "  epsilon=0.0001\n",
        "  gamma=100000\n",
        "  start_time=time.perf_counter()\n",
        "  svr = SVR(kernel='rbf',gamma=gamma,C=C,epsilon=epsilon)\n",
        "  svr.fit(X_scaled, y_scaled)\n",
        "  y_pred_svr=svr.predict(X_scaled)\n",
        "  predicted_prices_in_and_out=np.hstack((predicted_prices_in_and_out,y_pred_svr*y_scale+y_offset))\n",
        "\n",
        "  #Use SVR to predict out of sample\n",
        "  X2 = test[['moneyness','maturity']].values\n",
        "  X2 = np.asarray((X2 - X_offset) / X_scale).astype('float32')\n",
        "  y2 = test[['market price']].values.ravel()\n",
        "  y_pred_svr2=svr.predict(X2)\n",
        "  predicted_prices_in_and_out=np.hstack((predicted_prices_in_and_out,y_pred_svr2*y_scale+y_offset))\n",
        "\n",
        "  #Use SVR for full sample\n",
        "  all=pd.concat((train,test))\n",
        "  X = all[['moneyness','maturity']].values\n",
        "  X_offset = X.min(0)  # or X.mean(0)\n",
        "  X_scale = X.max(0) - X_offset  # or X.std(0)\n",
        "  X_scaled = np.asarray((X - X_offset) / X_scale).astype('float32')\n",
        "  y_all = all[['market price']].values.ravel()\n",
        "  y_all_offset = y_all.min(0)  # or X.mean(0)\n",
        "  y_all_scale = y_all.max(0) - y_all_offset  # or X.std(0)\n",
        "  y_all_scaled = np.asarray((y_all - y_all_offset) / y_all_scale).astype('float32')\n",
        "  svr = SVR(kernel='rbf',gamma=gamma,C=C,epsilon=epsilon)\n",
        "  svr.fit(X_scaled, y_all_scaled)\n",
        "  y_pred_all=svr.predict(X_scaled)\n",
        "  predicted_prices_all=np.hstack((predicted_prices_all,y_pred_all*y_all_scale+y_all_offset))\n",
        "\n",
        "  end_time=time.perf_counter()\n",
        "  mape_in=np.mean(np.divide(np.abs(y_pred_svr*y_scale+y_offset-y),y))\n",
        "  rmse_in=np.sqrt(np.mean((((y_pred_svr*y_scale+y_offset-y)**2))))\n",
        "  mape_out=np.mean(np.divide(np.abs(y_pred_svr2*y_scale+y_offset-y2),y2))\n",
        "  rmse_out=np.sqrt(np.mean((((y_pred_svr2*y_scale+y_offset-y2)**2))))\n",
        "\n",
        "  print(period + \" MAPE SVR in sample: \" + str(mape_in))\n",
        "  print(period + \" RMSE SVR in sample: \" + str(rmse_in))\n",
        "  print(period + \" MAPE SVR out sample: \" + str(mape_out))\n",
        "  print(period + \" RMSE SVR out sample: \" + str(rmse_out))\n",
        "  print(\"time \" + str(end_time-start_time))\n",
        "\n",
        "savetxt('svr_estimation.csv', predicted_prices_all, delimiter=',')\n",
        "files.download(\"svr_estimation.csv\")\n",
        "savetxt('svr_prediction.csv', predicted_prices_in_and_out, delimiter=',')\n",
        "files.download(\"svr_prediction.csv\")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "31071\n",
            "time for 1 option: 0.0012265719999504654\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6nnoc0MA-pb1"
      },
      "source": [
        "# least-squares Monte Carlo - Heston (LSM-Heston)\n",
        "\n",
        "This contains the steps seperately for testing, the full object oriented, commented code is in Class Heston\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8vAKSLXG3uOQ"
      },
      "source": [
        "1. Calibration step 1: kappa, eta and theta through indirect inference"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "bc1aMgiD32BY",
        "outputId": "574232e5-ad4a-4aed-e9c3-5d1c1b3bbff5"
      },
      "source": [
        "## Part 1: find kappa, eta and theta through indirect inference, as described in section 4.1 of AitSahlia ################################################################\n",
        "min_date=20030101\n",
        "max_date=20121231\n",
        "underlying_data=underlying_data[(underlying_data['numerical_date'] >= min_date) & (underlying_data['numerical_date'] <= max_date)]\n",
        "\n",
        "#Calculate (log) returns\n",
        "S=underlying_data[\"close\"].to_numpy()\n",
        "S_lag=shift(S,1,cval=np.NaN)\n",
        "r=np.log(np.divide(S,S_lag))*100\n",
        "r=r[1:]\n",
        "\n",
        "#Fit garch model to find ksi (the conditional kurtosis) (from page 345 in Engle and Lee (chapter 11))\n",
        "garch_model=arch.arch_model(r, mean='Zero', vol='GARCH', p=1, q=1, dist='t')\n",
        "model_fit = garch_model.fit()\n",
        "nu=model_fit.params.to_numpy()[3]\n",
        "ksi=3*(nu-2)/(nu-4)\n",
        "\n",
        "#Fit garch model to calculate Gamma_0\n",
        "garch_model=arch.arch_model(r, mean='Zero', vol='GARCH', p=1, q=1)\n",
        "model_fit = garch_model.fit()\n",
        "Gamma_0=model_fit.params.to_numpy()\n",
        "omega=Gamma_0[0]\n",
        "alpha=Gamma_0[1]\n",
        "beta=Gamma_0[2]\n",
        "print(\"for Gamma0: omega: \" + str(omega) + \"(3*10^-7) alpha: \" + str(alpha) + \"(0.04) beta: \" + str(beta) + \"(0.95), numbers in brackets are from AitSahlia\")\n",
        "\n",
        "#Set parameters as in AitSahlia page 195, equation 9, where we discretize time to 5 minutes\n",
        "N=len(r)\n",
        "discretizations=77\n",
        "tau=(1/discretizations)\n",
        "kappa_0=Gamma_0[0]/tau\n",
        "theta_0=(1-Gamma_0[1]-Gamma_0[2])/tau\n",
        "eta_0=Gamma_0[1]*np.sqrt((ksi-1)*tau) #Not there is a mistake in equation 9 in AitSahlia\n",
        "epsilon1=np.random.normal(0,1,[N*discretizations,1])\n",
        "epsilon2=np.random.normal(0,1,[N*discretizations,1])\n",
        "print(\"for Theta0: kappa: \" + str(kappa_0) + \"(0.0044) theta: \" + str(theta_0) + \"(6.93*10^-5) eta: \" + str(eta_0) + \"(0.0653), numbers in brackets are from AitSahlia\")\n",
        "\n",
        "#Function that generates data that follows the Heston model\n",
        "def generate_Heston(k_0,theta_0,eta_0,N,discretizations,tau,epsilon1,epsilon2):\n",
        "    r_gen=np.zeros([N,1])\n",
        "    v_0=0.187377 #Taken from AitSahlia\n",
        "    v_gen_dis=np.zeros([N*discretizations,1])\n",
        "    for t in range(0,N*discretizations):\n",
        "        if t==0:\n",
        "            v_gen_dis[t]=k_0*theta_0*tau+(1-k_0*tau)*v_0+eta_0*np.sqrt(tau*v_0)*epsilon2[t]\n",
        "        else:\n",
        "            v_gen_dis[t]=k_0*theta_0*tau+(1-k_0*tau)*v_gen_dis[t-1]+eta_0*np.sqrt(tau*v_gen_dis[t-1])*epsilon2[t]\n",
        "        if v_gen_dis[t]<0:\n",
        "            v_gen_dis[t]=-v_gen_dis[t]\n",
        "    r_gen_dis=np.multiply(np.sqrt(v_gen_dis*tau),epsilon1)\n",
        "    for n in range(0,N):\n",
        "      r_gen[n]=np.sum(r_gen_dis[n*discretizations:(n+1)*discretizations])\n",
        "    return r_gen\n",
        "\n",
        "r_gen=generate_Heston(kappa_0,theta_0,eta_0,N,discretizations,tau,epsilon1,epsilon2)\n",
        "\n",
        "#Fit garch model to calculate Gamma_1 \n",
        "garch_model=arch.arch_model(r_gen, mean='Zero', vol='GARCH', p=1, q=1)\n",
        "model_fit = garch_model.fit()\n",
        "Gamma_1=model_fit.params.to_numpy()\n",
        "\n",
        "plt.title('to get an idea of the simulated data: blue=real, red=generated under Theta_0, green=generated under Theta_1')\n",
        "plt.plot(r,'b')\n",
        "plt.plot(r_gen,'r')\n",
        "\n",
        "#Fit garch model with fixed parameters Gamma_1 \n",
        "garch_model=arch.arch_model(r, mean='Zero', vol='GARCH', p=1, q=1)\n",
        "fixed_fit=garch_model.fix(Gamma_1)\n",
        "conVol = fixed_fit.conditional_volatility\n",
        "resid = fixed_fit.resid\n",
        "\n",
        "#Function that calculates omega matrix, as in AitSahlia page 195 (where entries correspond to derivatives)\n",
        "def create_matrix(omega,alpha,beta,resid,conVol,r,N):\n",
        "    for t in range(1,N):\n",
        "        entry1=-1/(omega+alpha*resid[t-1]**2+beta*conVol[t-1])+(r[t]**2)/(2*(omega+alpha*resid[t-1]**2+beta*conVol[t-1])**2)\n",
        "        entry2=-(resid[t-1]**2)/(omega+alpha*resid[t-1]**2+beta*conVol[t-1])+(r[t]**2)*(resid[t-1]**2)/(2*(omega+alpha*resid[t-1]**2+beta*conVol[t-1])**2)\n",
        "        entry3=-conVol[t-1]/(omega+alpha*resid[t-1]**2+beta*conVol[t-1])+(r[t]**2)*conVol[t-1]/(2*(omega+alpha*resid[t-1]**2+beta*conVol[t-1])**2)\n",
        "        vec=[[entry1],[entry2],[entry3]]\n",
        "        if t==1:\n",
        "            sum=np.matmul(vec,np.transpose(vec))\n",
        "        else:\n",
        "            sum=sum+np.matmul(vec,np.transpose(vec))\n",
        "    return scipy.linalg.inv((1/N)*sum)\n",
        "\n",
        "omega=Gamma_1[0]\n",
        "alpha=Gamma_1[1]\n",
        "beta=Gamma_1[2]\n",
        "print(\"for Gamma1: omega: \" + str(omega) + \"(4*10^-9) alpha: \" + str(alpha) + \"(0.45) beta: \" + str(beta) + \"(0.55), numbers in brackets are from AitSahlia\")\n",
        "Omega=create_matrix(omega,alpha,beta,resid,conVol,r,N)\n",
        "\n",
        "#Function that calculates the criterium as in AitSahlia page 196, equation 11, using m from equation 10 (where entries correspond to derivatives)\n",
        "def OptFun(Theta_1,Gamma_1,Omega,omega,alpha,beta,N,discretizations,tau):\n",
        "    m=np.array([0, 0, 0])\n",
        "    kappa=Theta_1[0]\n",
        "    theta=Theta_1[1]\n",
        "    eta=Theta_1[2]\n",
        "    r_gen=generate_Heston(kappa,theta,eta,N,discretizations,tau,epsilon1,epsilon2)\n",
        "    garch_model=arch.arch_model(r_gen, mean='Zero', vol='GARCH', p=1, q=1)\n",
        "    fixed_fit=garch_model.fix(Gamma_1)\n",
        "    conVol = fixed_fit.conditional_volatility\n",
        "    resid = fixed_fit.resid\n",
        "    for t in range(1,N):\n",
        "        m[0]=m[0]-1/(omega+alpha*resid[t-1]**2+beta*conVol[t-1])+(r_gen[t]**2)/(2*(omega+alpha*resid[t-1]**2+beta*conVol[t-1])**2)\n",
        "        m[1]=m[1]-(resid[t-1]**2)/(omega+alpha*resid[t-1]**2+beta*conVol[t-1])+(r_gen[t]**2)*(resid[t-1]**2)/(2*(omega+alpha*resid[t-1]**2+beta*conVol[t-1])**2)\n",
        "        m[2]=m[2]-conVol[t-1]/(omega+alpha*resid[t-1]**2+beta*conVol[t-1])+(r_gen[t]**2)*conVol[t-1]/(2*(omega+alpha*resid[t-1]**2+beta*conVol[t-1])**2)\n",
        "    m=m/N\n",
        "    result=np.matmul(m.T,np.matmul(Omega,m))\n",
        "    return result\n",
        "    \n",
        "res=scipy.optimize.minimize(OptFun,x0=[kappa_0,theta_0,eta_0],args=(Gamma_1,Omega,omega,alpha,beta,N,discretizations,tau),bounds=((0, None),(0, None),(0, None)))\n",
        "\n",
        "#This solution should be the final parameters kappa, theta, eta\n",
        "solution=res.x\n",
        "kappa=solution[0]\n",
        "theta=solution[1]\n",
        "eta=solution[2]\n",
        "print(\"Final solution: kappa: \" + str(kappa) + \"(2.65) theta: \" + str(theta) + \"(0.029) eta: \" + str(eta) + \"(0.154), numbers in brackets are from AitSahlia\")\n",
        "print(\"Note the values are not similar, especially theta\")\n",
        "r_gen_final=generate_Heston(kappa,theta,eta,N,discretizations,tau,epsilon1,epsilon2)\n",
        "plt.plot(r_gen_final,'g')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Iteration:      1,   Func. Count:      6,   Neg. LLF: 3462.47596844589\n",
            "Iteration:      2,   Func. Count:     14,   Neg. LLF: 3458.646757984434\n",
            "Iteration:      3,   Func. Count:     21,   Neg. LLF: 3455.859327648929\n",
            "Iteration:      4,   Func. Count:     28,   Neg. LLF: 3450.870556079545\n",
            "Iteration:      5,   Func. Count:     35,   Neg. LLF: 3449.145363910649\n",
            "Iteration:      6,   Func. Count:     42,   Neg. LLF: 3448.8051177015723\n",
            "Iteration:      7,   Func. Count:     49,   Neg. LLF: 3448.1827463598693\n",
            "Iteration:      8,   Func. Count:     56,   Neg. LLF: 3447.0710740955765\n",
            "Iteration:      9,   Func. Count:     63,   Neg. LLF: 3446.713657325886\n",
            "Iteration:     10,   Func. Count:     70,   Neg. LLF: 3446.562163754563\n",
            "Iteration:     11,   Func. Count:     76,   Neg. LLF: 3446.5546469463197\n",
            "Iteration:     12,   Func. Count:     82,   Neg. LLF: 3446.5483619396427\n",
            "Iteration:     13,   Func. Count:     88,   Neg. LLF: 3446.5483371389428\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 3446.5483371389414\n",
            "            Iterations: 13\n",
            "            Function evaluations: 88\n",
            "            Gradient evaluations: 13\n",
            "Iteration:      1,   Func. Count:      5,   Neg. LLF: 3500.3904981498754\n",
            "Iteration:      2,   Func. Count:     12,   Neg. LLF: 3495.768772522755\n",
            "Iteration:      3,   Func. Count:     18,   Neg. LLF: 3491.6064728211086\n",
            "Iteration:      4,   Func. Count:     24,   Neg. LLF: 3490.010175838342\n",
            "Iteration:      5,   Func. Count:     30,   Neg. LLF: 3487.9476963958687\n",
            "Iteration:      6,   Func. Count:     36,   Neg. LLF: 3487.8535009358566\n",
            "Iteration:      7,   Func. Count:     42,   Neg. LLF: 3487.830337734661\n",
            "Iteration:      8,   Func. Count:     48,   Neg. LLF: 3487.6626382027725\n",
            "Iteration:      9,   Func. Count:     53,   Neg. LLF: 3487.656486437518\n",
            "Iteration:     10,   Func. Count:     58,   Neg. LLF: 3487.6563896565667\n",
            "Iteration:     11,   Func. Count:     63,   Neg. LLF: 3487.6563880786125\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 3487.656388078548\n",
            "            Iterations: 11\n",
            "            Function evaluations: 63\n",
            "            Gradient evaluations: 11\n",
            "for Gamma0: omega: 0.014730078362853526(3*10^-7) alpha: 0.08152793797172654(0.04) beta: 0.9055862432925071(0.95), numbers in brackets are from AitSahlia\n",
            "for Theta0: kappa: 1.1342160339397214(0.0044) theta: 0.9922080426540073(6.93*10^-5) eta: 0.018749316937338455(0.0653), numbers in brackets are from AitSahlia\n",
            "Iteration:      1,   Func. Count:      5,   Neg. LLF: 3546.8192794614556\n",
            "Iteration:      2,   Func. Count:     14,   Neg. LLF: 3546.819090159011\n",
            "Iteration:      3,   Func. Count:     19,   Neg. LLF: 3546.6873098321007\n",
            "Iteration:      4,   Func. Count:     25,   Neg. LLF: 3546.6838571271956\n",
            "Iteration:      5,   Func. Count:     31,   Neg. LLF: 3546.680858280267\n",
            "Iteration:      6,   Func. Count:     37,   Neg. LLF: 3546.6797932095\n",
            "Iteration:      7,   Func. Count:     43,   Neg. LLF: 3546.678004825396\n",
            "Iteration:      8,   Func. Count:     48,   Neg. LLF: 3546.677968422347\n",
            "Iteration:      9,   Func. Count:     53,   Neg. LLF: 3546.677942496951\n",
            "Iteration:     10,   Func. Count:     58,   Neg. LLF: 3546.677881821492\n",
            "Iteration:     11,   Func. Count:     63,   Neg. LLF: 3546.6778085500264\n",
            "Iteration:     12,   Func. Count:     68,   Neg. LLF: 3546.6777938242667\n",
            "Optimization terminated successfully.    (Exit mode 0)\n",
            "            Current function value: 3546.677793295297\n",
            "            Iterations: 12\n",
            "            Function evaluations: 69\n",
            "            Gradient evaluations: 12\n",
            "for Gamma1: omega: 0.22369927944008122(4*10^-9) alpha: 0.0010695441145524046(0.45) beta: 0.7709798597867767(0.55), numbers in brackets are from AitSahlia\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "error",
          "ename": "KeyboardInterrupt",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-29-fb9cd851207d>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m    108\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mresult\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    109\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 110\u001b[0;31m \u001b[0mres\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mscipy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0moptimize\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mminimize\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mOptFun\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mx0\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mkappa_0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mtheta_0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0meta_0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mGamma_1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mOmega\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0momega\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0malpha\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mbeta\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mN\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mdiscretizations\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mtau\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mbounds\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    111\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    112\u001b[0m \u001b[0;31m#This solution should be the final parameters kappa, theta, eta\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/scipy/optimize/_minimize.py\u001b[0m in \u001b[0;36mminimize\u001b[0;34m(fun, x0, args, method, jac, hess, hessp, bounds, constraints, tol, callback, options)\u001b[0m\n\u001b[1;32m    608\u001b[0m     \u001b[0;32melif\u001b[0m \u001b[0mmeth\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'l-bfgs-b'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    609\u001b[0m         return _minimize_lbfgsb(fun, x0, args, jac, bounds,\n\u001b[0;32m--> 610\u001b[0;31m                                 callback=callback, **options)\n\u001b[0m\u001b[1;32m    611\u001b[0m     \u001b[0;32melif\u001b[0m \u001b[0mmeth\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'tnc'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    612\u001b[0m         return _minimize_tnc(fun, x0, args, jac, bounds, callback=callback,\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/scipy/optimize/lbfgsb.py\u001b[0m in \u001b[0;36m_minimize_lbfgsb\u001b[0;34m(fun, x0, args, jac, bounds, disp, maxcor, ftol, gtol, eps, maxfun, maxiter, iprint, callback, maxls, **unknown_options)\u001b[0m\n\u001b[1;32m    343\u001b[0m             \u001b[0;31m# until the completion of the current minimization iteration.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    344\u001b[0m             \u001b[0;31m# Overwrite f and g:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 345\u001b[0;31m             \u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mg\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfunc_and_grad\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    346\u001b[0m         \u001b[0;32melif\u001b[0m \u001b[0mtask_str\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstartswith\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34mb'NEW_X'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    347\u001b[0m             \u001b[0;31m# new iteration\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/scipy/optimize/lbfgsb.py\u001b[0m in \u001b[0;36mfunc_and_grad\u001b[0;34m(x)\u001b[0m\n\u001b[1;32m    288\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mjac\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    289\u001b[0m         \u001b[0;32mdef\u001b[0m \u001b[0mfunc_and_grad\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 290\u001b[0;31m             \u001b[0mf\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    291\u001b[0m             \u001b[0mg\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_approx_fprime_helper\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfun\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mepsilon\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mf0\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    292\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mg\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/scipy/optimize/optimize.py\u001b[0m in \u001b[0;36mfunction_wrapper\u001b[0;34m(*wrapper_args)\u001b[0m\n\u001b[1;32m    325\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mfunction_wrapper\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mwrapper_args\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    326\u001b[0m         \u001b[0mncalls\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 327\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mfunction\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mwrapper_args\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    328\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    329\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mncalls\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfunction_wrapper\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m<ipython-input-29-fb9cd851207d>\u001b[0m in \u001b[0;36mOptFun\u001b[0;34m(Theta_1, Gamma_1, Omega, omega, alpha, beta, N, discretizations, tau)\u001b[0m\n\u001b[1;32m     95\u001b[0m     \u001b[0mtheta\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mTheta_1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     96\u001b[0m     \u001b[0meta\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mTheta_1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 97\u001b[0;31m     \u001b[0mr_gen\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mgenerate_Heston\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkappa\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mtheta\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0meta\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mN\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mdiscretizations\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mtau\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mepsilon1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mepsilon2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     98\u001b[0m     \u001b[0mgarch_model\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0march\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0march_model\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mr_gen\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmean\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'Zero'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvol\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'GARCH'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mp\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mq\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     99\u001b[0m     \u001b[0mfixed_fit\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mgarch_model\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfix\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mGamma_1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m<ipython-input-29-fb9cd851207d>\u001b[0m in \u001b[0;36mgenerate_Heston\u001b[0;34m(k_0, theta_0, eta_0, N, discretizations, tau, epsilon1, epsilon2)\u001b[0m\n\u001b[1;32m     45\u001b[0m             \u001b[0mv_gen_dis\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mt\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mk_0\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mtheta_0\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mtau\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mk_0\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mtau\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mv_0\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0meta_0\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msqrt\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtau\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mv_0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mepsilon2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mt\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     46\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 47\u001b[0;31m             \u001b[0mv_gen_dis\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mt\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mk_0\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mtheta_0\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mtau\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mk_0\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mtau\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mv_gen_dis\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mt\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0meta_0\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msqrt\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtau\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mv_gen_dis\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mt\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mepsilon2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mt\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     48\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mv_gen_dis\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mt\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m<\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     49\u001b[0m             \u001b[0mv_gen_dis\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mt\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mv_gen_dis\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mt\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5fNoTX6039Z4"
      },
      "source": [
        "2. Calibration step 2: v, lamda, rho through minimizing error of european options"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 423
        },
        "id": "NEtHulQv38dD",
        "outputId": "8b04c205-5beb-40d9-f4e6-f9cfae95f556"
      },
      "source": [
        "## Part 2: find v, lamda, rho through minimizing squared pricing error ################################################################\n",
        "\n",
        "#Use paramters found in step 1\n",
        "k_1=kappa\n",
        "theta_1=theta\n",
        "eta_1=eta\n",
        "Theta_1=[k_1,theta_1,eta_1]\n",
        "\n",
        "#Functions necessary to find the put price, as in AitSahlia equation 4, index refers to j=1 or j=2\n",
        "def put_price(K,x,v,T,r,kappa,theta,eta,lamda,rho):\n",
        "    call_price=calcFFT(x,K,r,T,v,kappa,theta,eta,lamda,rho)\n",
        "    #Use put call parity\n",
        "    return call_price+K*np.exp(-r*T)-x\n",
        "\n",
        "def calcFFT(x,K,r,T,v,kappa,theta,eta,lamda,rho):\n",
        "    alpha = 4\n",
        "    N=2**12\n",
        "    Upperlimit=1000\n",
        "    etaa=Upperlimit/N\n",
        "    lambdaFFT=(2*np.pi)/(N*etaa)\n",
        "    b=N*lambdaFFT/2\n",
        "    u=np.linspace(0,N-1,N)*etaa\n",
        "    KGrid = -b+lambdaFFT*np.linspace(0,N-1,N)\n",
        "    help_vec=np.zeros([N])\n",
        "    help_vec[0]=1\n",
        "    #Carr-Madan Equation\n",
        "    Psi=np.exp(-r*T)*np.divide(HestonCF(u-(alpha+1)*complex(0,1),x,r,T,v,kappa,theta,eta,rho,lamda),(alpha**2+alpha-np.multiply(u,u)+complex(0,1)*(2*alpha+1)*u))\n",
        "    Function=np.multiply(np.exp(complex(0,1)*b*u),np.multiply(Psi,((etaa/3)*(3+np.power(-1,np.linspace(1,N,N))-help_vec))))\n",
        "    FastFourierPriceGrid=(np.exp(-KGrid*alpha)/np.pi)*np.real(np.fft.fft(Function))\n",
        "    SpotOnGrid = (np.log(K)+b)/lambdaFFT+1\n",
        "    return (1-(SpotOnGrid-np.floor(SpotOnGrid)))*FastFourierPriceGrid[int(np.floor(SpotOnGrid))-1]+(SpotOnGrid-np.floor(SpotOnGrid))*FastFourierPriceGrid[int(np.floor(SpotOnGrid))]\n",
        "    \n",
        "def HestonCF(Phi,S0,r,T,V0,kappa,theta,sigma,rho,lamda):\n",
        "    a=kappa*theta\n",
        "    u=-0.5\n",
        "    b = kappa+lamda\n",
        "    d=np.sqrt((rho*sigma*complex(0,1)*Phi-b)**2-sigma**2*(2*u*complex(0,1)*Phi-Phi**2))\n",
        "    g=(b-rho*sigma*complex(0,1)*Phi-d)/(b-rho*sigma*complex(0,1)*Phi+d)\n",
        "    D=(b-rho*sigma*complex(0,1)*Phi-d)/(sigma**2*(1-np.exp(-d*T))/(1-g*np.exp(-d*T)))\n",
        "    C=r*complex(0,1)*Phi*T+(a/(sigma**2))*((b-rho*sigma*complex(0,1)*Phi-d)*T-2*np.log(((1-g*np.exp(-d*T))/(1-g))))            \n",
        "    return_value=np.exp(C+D*V0+complex(0,1)*Phi*np.log(S0))\n",
        "    return return_value\n",
        "\n",
        "#function that defines optimization criterium\n",
        "def sum_squared_error(params,day_data,kappa,theta,eta):\n",
        "    #print('calculating SSE')\n",
        "    v=params[0]\n",
        "    rho=params[1]\n",
        "    lamda=0\n",
        "    SSE=0\n",
        "    for index, row in day_data.iterrows():\n",
        "        real_price=row['market price']\n",
        "        estimated_price=put_price(row['strike_price'],row['underlying'],v,row['maturity'],0,kappa,theta,eta,lamda,rho)\n",
        "        SSE=SSE+(real_price-estimated_price)**2\n",
        "    if (math.isnan(SSE)):\n",
        "        SSE=10**20\n",
        "    return SSE\n",
        "\n",
        "#Optimize parameters for every trading day\n",
        "date_vec=option_data_european[\"date\"].to_numpy()\n",
        "days=len(set(option_data_european[\"date\"].to_numpy()))\n",
        "days=10\n",
        "v_vec=np.zeros([days,1])\n",
        "rho_vec=np.zeros([days,1])\n",
        "lamda_vec=np.zeros([days,1])\n",
        "day_selector=0\n",
        "\n",
        "for day in range(0,days):\n",
        "    if (day%1==0):\n",
        "      print(\"day: \" + str(day) + \" of \" + str(days-1))\n",
        "    \n",
        "    #Set initial parameters\n",
        "    if day==0:\n",
        "        date=date_vec[day_selector]\n",
        "        v0=0.0349\n",
        "        rho0=-0.487\n",
        "        lamda0=2.14 \n",
        "    else:\n",
        "        while (date_vec[day_selector]==prev_date):\n",
        "            day_selector=day_selector+1\n",
        "        date=date_vec[day_selector]\n",
        "        v0=v_vec[day-1]\n",
        "        rho0=rho_vec[day-1]\n",
        "        lamda0=lamda_vec[day-1]\n",
        "    params0=[v0,rho0,lamda0]\n",
        "    \n",
        "    #select the correct options\n",
        "    day_data = option_data_european[(option_data_european['date']==date)]\n",
        "    #Minimize for these options\n",
        "    res=scipy.optimize.minimize(sum_squared_error,x0=[v0,rho0],args=(day_data,k_1,theta_1,eta_1),bounds=((0, 1),(-0.8,0.8)),options={'maxiter': 20})\n",
        "    solution=res.x\n",
        "    v_vec[day]=solution[0]\n",
        "    rho_vec[day]=solution[1]\n",
        "    #lamda_vec[day]=solution[2]\n",
        "    prev_date=date\n",
        "\n",
        "#This solution should be the final parameters v, rho, lamda     \n",
        "v=np.mean(v_vec)\n",
        "rho=np.mean(rho_vec)\n",
        "print(\"v: \" + str(v) + \"(0.03) rho: \" + str(rho) + \"(-0.49), numbers in brackets are from AitSahlia\")\n",
        "#No MAXITER on full sample: v: 0.0022569100134651613(0.03) rho: -0.3812581643813785(-0.49), numbers in brackets are from AitSahlia "
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "day: 0 of 9\n",
            "day: 1 of 9\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "error",
          "ename": "KeyboardInterrupt",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-29-fa69c81130ec>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     89\u001b[0m     \u001b[0mday_data\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0moption_data_european\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0moption_data_european\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'date'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m==\u001b[0m\u001b[0mdate\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     90\u001b[0m     \u001b[0;31m#Minimize for these options\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 91\u001b[0;31m     \u001b[0mres\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mscipy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0moptimize\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mminimize\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msum_squared_error\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mx0\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mv0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mrho0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mday_data\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mk_1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mtheta_1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0meta_1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mbounds\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m0.8\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0.8\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0moptions\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m{\u001b[0m\u001b[0;34m'maxiter'\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;36m20\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     92\u001b[0m     \u001b[0msolution\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mres\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     93\u001b[0m     \u001b[0mv_vec\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mday\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0msolution\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/scipy/optimize/_minimize.py\u001b[0m in \u001b[0;36mminimize\u001b[0;34m(fun, x0, args, method, jac, hess, hessp, bounds, constraints, tol, callback, options)\u001b[0m\n\u001b[1;32m    608\u001b[0m     \u001b[0;32melif\u001b[0m \u001b[0mmeth\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'l-bfgs-b'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    609\u001b[0m         return _minimize_lbfgsb(fun, x0, args, jac, bounds,\n\u001b[0;32m--> 610\u001b[0;31m                                 callback=callback, **options)\n\u001b[0m\u001b[1;32m    611\u001b[0m     \u001b[0;32melif\u001b[0m \u001b[0mmeth\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'tnc'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    612\u001b[0m         return _minimize_tnc(fun, x0, args, jac, bounds, callback=callback,\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/scipy/optimize/lbfgsb.py\u001b[0m in \u001b[0;36m_minimize_lbfgsb\u001b[0;34m(fun, x0, args, jac, bounds, disp, maxcor, ftol, gtol, eps, maxfun, maxiter, iprint, callback, maxls, **unknown_options)\u001b[0m\n\u001b[1;32m    343\u001b[0m             \u001b[0;31m# until the completion of the current minimization iteration.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    344\u001b[0m             \u001b[0;31m# Overwrite f and g:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 345\u001b[0;31m             \u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mg\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfunc_and_grad\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    346\u001b[0m         \u001b[0;32melif\u001b[0m \u001b[0mtask_str\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstartswith\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34mb'NEW_X'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    347\u001b[0m             \u001b[0;31m# new iteration\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/scipy/optimize/lbfgsb.py\u001b[0m in \u001b[0;36mfunc_and_grad\u001b[0;34m(x)\u001b[0m\n\u001b[1;32m    289\u001b[0m         \u001b[0;32mdef\u001b[0m \u001b[0mfunc_and_grad\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    290\u001b[0m             \u001b[0mf\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 291\u001b[0;31m             \u001b[0mg\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_approx_fprime_helper\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfun\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mepsilon\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mf0\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    292\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mg\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    293\u001b[0m     \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/scipy/optimize/optimize.py\u001b[0m in \u001b[0;36m_approx_fprime_helper\u001b[0;34m(xk, f, epsilon, args, f0)\u001b[0m\n\u001b[1;32m    695\u001b[0m         \u001b[0mei\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m1.0\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    696\u001b[0m         \u001b[0md\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mepsilon\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mei\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 697\u001b[0;31m         \u001b[0mdf\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mxk\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0md\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mf0\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0md\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    698\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0misscalar\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdf\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    699\u001b[0m             \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/scipy/optimize/optimize.py\u001b[0m in \u001b[0;36mfunction_wrapper\u001b[0;34m(*wrapper_args)\u001b[0m\n\u001b[1;32m    325\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mfunction_wrapper\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mwrapper_args\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    326\u001b[0m         \u001b[0mncalls\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 327\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mfunction\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mwrapper_args\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    328\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    329\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mncalls\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfunction_wrapper\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m<ipython-input-29-fa69c81130ec>\u001b[0m in \u001b[0;36msum_squared_error\u001b[0;34m(params, day_data, kappa, theta, eta)\u001b[0m\n\u001b[1;32m     52\u001b[0m     \u001b[0;32mfor\u001b[0m \u001b[0mindex\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrow\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mday_data\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0miterrows\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     53\u001b[0m         \u001b[0mreal_price\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mrow\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'market price'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 54\u001b[0;31m         \u001b[0mestimated_price\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mput_price\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrow\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'strike_price'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mrow\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'underlying'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mv\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mrow\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'maturity'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mkappa\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mtheta\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0meta\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mlamda\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mrho\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     55\u001b[0m         \u001b[0mSSE\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mSSE\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mreal_price\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mestimated_price\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     56\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mmath\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0misnan\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mSSE\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m<ipython-input-29-fa69c81130ec>\u001b[0m in \u001b[0;36mput_price\u001b[0;34m(K, x, v, T, r, kappa, theta, eta, lamda, rho)\u001b[0m\n\u001b[1;32m     10\u001b[0m \u001b[0;31m#Functions necessary to find the put price, as in AitSahlia equation 4, index refers to j=1 or j=2\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     11\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mput_price\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mK\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mv\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mT\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mr\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mkappa\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mtheta\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0meta\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mlamda\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mrho\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 12\u001b[0;31m     \u001b[0mcall_price\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mcalcFFT\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mK\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mr\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mT\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mv\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mkappa\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mtheta\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0meta\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mlamda\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mrho\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     13\u001b[0m     \u001b[0;31m#Use put call parity\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     14\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mcall_price\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0mK\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mr\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mT\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m<ipython-input-29-fa69c81130ec>\u001b[0m in \u001b[0;36mcalcFFT\u001b[0;34m(x, K, r, T, v, kappa, theta, eta, lamda, rho)\u001b[0m\n\u001b[1;32m     27\u001b[0m     \u001b[0;31m#Carr-Madan Equation\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     28\u001b[0m     \u001b[0mPsi\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mr\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mT\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdivide\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mHestonCF\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mu\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0malpha\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mcomplex\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mr\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mT\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mv\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mkappa\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mtheta\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0meta\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mrho\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mlamda\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0malpha\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0malpha\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmultiply\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mu\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mu\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0mcomplex\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0malpha\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mu\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 29\u001b[0;31m     \u001b[0mFunction\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmultiply\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcomplex\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mb\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mu\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmultiply\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mPsi\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0metaa\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpower\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlinspace\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mN\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mN\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mhelp_vec\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     30\u001b[0m     \u001b[0mFastFourierPriceGrid\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mKGrid\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0malpha\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfft\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfft\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mFunction\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     31\u001b[0m     \u001b[0mSpotOnGrid\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlog\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mK\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0mb\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0mlambdaFFT\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "44cIhcOyRdJe"
      },
      "source": [
        "2. Pricing step: price american options, using the calibrated model\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Zk0gkOt3Rkxz",
        "outputId": "c806c3d7-7d5e-4a81-ca1d-25ff2f974df9"
      },
      "source": [
        "#### part 3\n",
        "def L0(X):\n",
        "  return np.exp(-X/2)\n",
        "def L1(X):\n",
        "  return np.multiply(np.exp(-X/2),(1-X))\n",
        "def L2(X):\n",
        "  return (1/2)*np.multiply(np.exp(-X/2),(np.multiply(X,X)-4*X+2))\n",
        "\n",
        "max_vec=np.vectorize(max,otypes=[np.float64])\n",
        "\n",
        "#parameters of heston model\n",
        "v=0.0349\n",
        "rho=-0.487\n",
        "lamda=0\n",
        "kappa=0.023 #(2.65)\n",
        "theta=0.018 #(0.029)\n",
        "eta=0.277   #(0.154)\n",
        "print(2*kappa*theta-eta**2)\n",
        "N=1000 #amount of paths (100000)\n",
        "m=50\n",
        "\n",
        "epsilon=np.random.multivariate_normal([0,0],[[1,rho],[rho,1]],[m,N])\n",
        "\n",
        "def generate_Heston_matrix(v_0,rho,lamda,kappa,theta,eta,m,N,S_0,h,epsilon):\n",
        "    S_paths=np.zeros([N,m])\n",
        "    #Multiply epsilon by h to deal with the timestep\n",
        "    epsilon=epsilon*np.sqrt(h)\n",
        "    v_0=v_0*np.ones([1,N])\n",
        "    for ti in range(0,m):\n",
        "        if ti==0:\n",
        "            v=kappa*theta+(1-kappa)*v_0+eta*np.sqrt(v_0)*epsilon[ti,:,1]\n",
        "            v=abs(v)\n",
        "            S=np.exp(np.multiply(np.sqrt(v),epsilon[ti,:,0]))*S_0\n",
        "            S_paths[:,ti]=S\n",
        "        else:\n",
        "            v=kappa*theta+(1-kappa)*v+eta*np.sqrt(v)*epsilon[ti,:,1]\n",
        "            v=abs(v)\n",
        "            S=np.exp(np.multiply(np.sqrt(v),epsilon[ti,:,0]))*S_0\n",
        "            S_paths[:,ti]=S\n",
        "    return S_paths\n",
        "\n",
        "def price_option_LSM(S_0,K,maturity,r,epsilon):\n",
        "    #I'm not exactly sure how to handle the timestep\n",
        "    h=maturity/m\n",
        "\n",
        "    #simulate path\n",
        "    S_paths=generate_Heston_matrix(v,rho,lamda,kappa,theta,eta,m,N,S_0,h,epsilon)\n",
        "   \n",
        "    start_cashflow_time=time.perf_counter() \n",
        "    #create matrix of cashflows, and matrix of discount rates\n",
        "\n",
        "    cashflow_matrix=np.zeros([N,m])\n",
        "    discount_matrix=np.ones([N,m])\n",
        "    for ti in range(0,m):\n",
        "        discount_matrix[:,ti]=discount_matrix[:,ti]*np.exp(-r*ti)    \n",
        "    cashflow_matrix[:,m-1]=max_vec(K-S_paths[:,m-1],0)\n",
        "\n",
        "    #recursively calculate the cashflows\n",
        "    for ti in range(m-2,-1,-1):\n",
        "        exercise_value=max_vec(K-S_paths[:,ti],0)\n",
        "        #calculate continuation value by regressing in the money options\n",
        "        itm_indices=np.where(exercise_value > 0)[0]\n",
        "        if (np.shape(itm_indices)[0]>0):\n",
        "          Y=np.matmul(np.multiply(cashflow_matrix,discount_matrix),np.ones([m,1]))\n",
        "          X=np.column_stack([np.zeros([N,1]),L0(S_paths[:,ti]),L1(S_paths[:,ti]),L2(S_paths[:,ti])])\n",
        "          end_Xregression_matrix_time=time.perf_counter()\n",
        "          Y_itm=Y[itm_indices]\n",
        "          X_itm=X[itm_indices,:]\n",
        "          beta=np.linalg.lstsq(np.matmul(X_itm.T,X_itm),np.matmul(X_itm.T,Y_itm),rcond=1)[0]\n",
        "          continuation_value=np.matmul(X,beta)\n",
        "          exercise_indices=np.where((exercise_value>continuation_value[0,:])*1 == 1)[0]\n",
        "          cashflow_matrix[exercise_indices,:]=np.zeros([len(exercise_indices),m])\n",
        "          cashflow_matrix[exercise_indices,ti]=exercise_value[exercise_indices]\n",
        "\n",
        "    #the option price is the mean of the discounted cashflows\n",
        "    option_value=np.mean(np.matmul(np.multiply(cashflow_matrix,discount_matrix),np.ones([m,1])))\n",
        "    return option_value\n",
        "\n",
        "#Price the options\n",
        "i=0\n",
        "rows=np.shape(option_data)[0]\n",
        "\n",
        "amount=10000\n",
        "mape=0\n",
        "total_time=0\n",
        "for index, row in option_data.iterrows():\n",
        "  i=i+1\n",
        "  if (i>amount):\n",
        "    break\n",
        "  if (i%(amount/10)==0):\n",
        "    print(i)\n",
        "  start_price_time=time.perf_counter() \n",
        "  estimated_option_value=price_option_LSM(row[\"underlying\"],row[\"strike_price\"],row[\"maturity\"],row[\"interest_rate\"]/250,epsilon)\n",
        "  end_price_time=time.perf_counter() \n",
        "  total_time=total_time+end_price_time-start_price_time\n",
        "  #print(\"Time to price option: \" + str(end_price_time-start_price_time))\n",
        "  true_option_value=row[\"market price\"]\n",
        "  #print(\"underlying: \"  + str(row[\"underlying\"]) + \" strike: \" + str(row[\"strike_price\"]) + \" maturity: \" + str(row[\"maturity\"]))\n",
        "  #print(\"estimated: \"  + str(estimated_option_value) + \" true: \" + str(true_option_value))\n",
        "  mape=mape+(1/amount)*(np.abs(estimated_option_value-true_option_value)/true_option_value)\n",
        "print(\"MAPE: \" + str(mape))\n",
        "print(\"total time: \" + str(total_time) + \", time per option: \" + str(total_time/amount))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "-0.07590100000000002\n",
            "1000\n",
            "2000\n",
            "3000\n",
            "4000\n",
            "5000\n",
            "6000\n",
            "7000\n",
            "8000\n",
            "9000\n",
            "10000\n",
            "MAPE: 0.8084202129298442\n",
            "total time: 413.88203647086993, time per option: 0.041388203647086994\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "G-qQU4zrNwaF"
      },
      "source": [
        "0.806167"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5JSoP71viFN3"
      },
      "source": [
        "# Class Heston"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KmAxxpcaA_X3"
      },
      "source": [
        "class HestonModel():\n",
        "    \n",
        "    def __init__(self,\n",
        "                 option_data_european,\n",
        "                 underlying_data):\n",
        "        \n",
        "        self.underlying_data=underlying_data\n",
        "        self.option_data_european=option_data_european\n",
        "                 \n",
        "    def calibrate_structural(self):\n",
        "       '''\n",
        "       First step of heston calibration, calculates kappa, theta and eta\n",
        "       '''\n",
        "        min_date=20030101\n",
        "        max_date=20121231\n",
        "        self.underlying_data=self.underlying_data[(self.underlying_data['numerical_date'] >= min_date) & (self.underlying_data['numerical_date'] <= max_date)]\n",
        "        \n",
        "        #Calculate (log) returns\n",
        "        S=self.underlying_data[\"close\"].to_numpy()\n",
        "        S_lag=shift(S,1,cval=np.NaN)\n",
        "        r=np.log(np.divide(S,S_lag))*100\n",
        "        r=r[1:]\n",
        "\n",
        "        plt.plot(r, 'b')\n",
        "\n",
        "        #Fit garch model to find ksi (the conditional kurtosis) (from page 345 in Engle and Lee (chapter 11))\n",
        "        garch_model=arch.arch_model(r, mean='Zero', vol='GARCH', p=1, q=1, dist='t')\n",
        "        model_fit = garch_model.fit(disp=\"off\")\n",
        "        nu=model_fit.params.to_numpy()[3]\n",
        "        ksi=3*(nu-2)/(nu-4)\n",
        "        \n",
        "        #Fit garch model to calculate Gamma_0\n",
        "        garch_model=arch.arch_model(r, mean='Zero', vol='GARCH', p=1, q=1)\n",
        "        model_fit = garch_model.fit(disp=\"off\")\n",
        "        Gamma_0=model_fit.params.to_numpy()\n",
        "        omega=Gamma_0[0]\n",
        "        alpha=Gamma_0[1]\n",
        "        beta=Gamma_0[2]\n",
        "        print(\"for Gamma0: omega: \" + str(omega) + \"(3*10^-7) alpha: \" + str(alpha) + \"(0.04) beta: \" + str(beta) + \"(0.95), numbers in brackets are from AitSahlia\")\n",
        "        \n",
        "        #Set parameters as in AitSahlia page 195, equation 9, where we discretize time to 5 minutes\n",
        "        N=len(r)\n",
        "        discretizations=1\n",
        "        tau=(1/discretizations)\n",
        "        kappa_0=Gamma_0[0]/(1-Gamma_0[1]-Gamma_0[2])\n",
        "        theta_0=(1-Gamma_0[1]-Gamma_0[2])/tau\n",
        "        eta_0=Gamma_0[1]*np.sqrt((ksi-1)*tau) #Note there is a mistake in equation 9 in AitSahlia\n",
        "        print(\"for Theta0: kappa: \" + str(kappa_0) + \"(0.0044) theta: \" + str(theta_0) + \"(6.93*10^-5) eta: \" + str(eta_0) + \"(0.0653), numbers in brackets are from AitSahlia\")\n",
        "        epsilon1=np.random.normal(0,1,[N*discretizations,1])\n",
        "        epsilon2=np.random.normal(0,1,[N*discretizations,1])           \n",
        "        r_gen=self.generate_Heston(kappa_0,theta_0,eta_0,N,discretizations,tau,epsilon1,epsilon2)\n",
        "\n",
        "        plt.plot(r_gen,'r')\n",
        "\n",
        "        #Fit garch model to calculate Gamma_1 \n",
        "        garch_model=arch.arch_model(r_gen, mean='Zero', vol='GARCH', p=1, q=1)\n",
        "        model_fit = garch_model.fit(disp=\"off\")\n",
        "        Gamma_1=model_fit.params.to_numpy()\n",
        "        \n",
        "        #Fit garch model with fixed parameters Gamma_1 \n",
        "        garch_model=arch.arch_model(r, mean='Zero', vol='GARCH', p=1, q=1)\n",
        "        fixed_fit=garch_model.fix(Gamma_1)\n",
        "        conVol = fixed_fit.conditional_volatility\n",
        "        resid = fixed_fit.resid            \n",
        "        omega=Gamma_1[0]\n",
        "        alpha=Gamma_1[1]\n",
        "        beta=Gamma_1[2]\n",
        "        print(\"for Gamma1: omega: \" + str(omega) + \"(4*10^-9) alpha: \" + str(alpha) + \"(0.45) beta: \" + str(beta) + \"(0.55), numbers in brackets are from AitSahlia\")\n",
        "        Omega=self.create_matrix(omega,alpha,beta,resid,conVol,r,N)\n",
        "            \n",
        "        epsilon1=np.random.normal(0,1,[N*discretizations,1])\n",
        "        epsilon2=np.random.normal(0,1,[N*discretizations,1])  \n",
        "      \n",
        "        res=scipy.optimize.minimize(self.OptFun,x0=[kappa_0,theta_0,eta_0],args=(Gamma_1,Omega,omega,alpha,beta,N,discretizations,tau,epsilon1,epsilon2),bounds=((0, None),(0, 2),(0, 2)))\n",
        "        #This solution should be the final parameters kappa, theta, eta\n",
        "        solution=res.x\n",
        "        kappa=solution[0]\n",
        "        theta=solution[1]\n",
        "        eta=solution[2]\n",
        "        print(\"Final solution=Theta1: kappa: \" + str(kappa) + \"(2.65) theta: \" + str(theta) + \"(0.029) eta: \" + str(eta) + \"(0.154), numbers in brackets are from AitSahlia\")\n",
        "        return solution\n",
        "                    \n",
        "    #Function that generates data that follows the Heston model\n",
        "    def generate_Heston(self,k_0,theta_0,eta_0,N,discretizations,tau,epsilon1,epsilon2):\n",
        "      '''\n",
        "      Generates data according to the Heston model\n",
        "      '''\n",
        "        r_gen=np.zeros([N,1])\n",
        "        v_0=0.187377 #Taken from AitSahlia\n",
        "        v_gen_dis=np.zeros([N*discretizations,1])\n",
        "        for t in range(0,N*discretizations):\n",
        "            if t==0:\n",
        "                v_gen_dis[t]=k_0*theta_0*tau+(1-k_0*tau)*v_0+eta_0*np.sqrt(tau*v_0)*epsilon2[t]\n",
        "            else:\n",
        "                v_gen_dis[t]=k_0*theta_0*tau+(1-k_0*tau)*v_gen_dis[t-1]+eta_0*np.sqrt(tau*v_gen_dis[t-1])*epsilon2[t]\n",
        "            if v_gen_dis[t]<0:\n",
        "                v_gen_dis[t]=-v_gen_dis[t]\n",
        "        r_gen_dis=np.multiply(np.sqrt(v_gen_dis*tau),epsilon1)\n",
        "        for n in range(0,N):\n",
        "          r_gen[n]=np.sum(r_gen_dis[n*discretizations:(n+1)*discretizations])\n",
        "        return r_gen    \n",
        "    \n",
        "    #Function that calculates omega matrix, as in AitSahlia page 195 (where entries correspond to derivatives)\n",
        "    def create_matrix(self,omega,alpha,beta,resid,conVol,r,N):\n",
        "      '''\n",
        "      Creates Omega matrix\n",
        "      '''\n",
        "        for t in range(1,N):\n",
        "            entry1=-1/(omega+alpha*resid[t-1]**2+beta*conVol[t-1])+(r[t]**2)/(2*(omega+alpha*resid[t-1]**2+beta*conVol[t-1])**2)\n",
        "            entry2=-(resid[t-1]**2)/(omega+alpha*resid[t-1]**2+beta*conVol[t-1])+(r[t]**2)*(resid[t-1]**2)/(2*(omega+alpha*resid[t-1]**2+beta*conVol[t-1])**2)\n",
        "            entry3=-conVol[t-1]/(omega+alpha*resid[t-1]**2+beta*conVol[t-1])+(r[t]**2)*conVol[t-1]/(2*(omega+alpha*resid[t-1]**2+beta*conVol[t-1])**2)\n",
        "            vec=[[entry1],[entry2],[entry3]]\n",
        "            if t==1:\n",
        "                sum=np.matmul(vec,np.transpose(vec))\n",
        "            else:\n",
        "                sum=sum+np.matmul(vec,np.transpose(vec))\n",
        "        return scipy.linalg.inv((1/N)*sum)\n",
        "    \n",
        "    #Function that calculates the criterium as in AitSahlia page 196, equation 11, using m from equation 10 (where entries correspond to derivatives)\n",
        "    def OptFun(self,Theta_1,Gamma_1,Omega,omega,alpha,beta,N,discretizations,tau,epsilon1,epsilon2):\n",
        "      '''\n",
        "      Optimization criterium\n",
        "      '''\n",
        "        m=np.array([0, 0, 0])\n",
        "        kappa=Theta_1[0]\n",
        "        theta=Theta_1[1]\n",
        "        eta=Theta_1[2]\n",
        "        r_gen=self.generate_Heston(kappa,theta,eta,N,discretizations,tau,epsilon1,epsilon2)\n",
        "        garch_model=arch.arch_model(r_gen, mean='Zero', vol='GARCH', p=1, q=1)\n",
        "        fixed_fit=garch_model.fix(Gamma_1)\n",
        "        conVol = fixed_fit.conditional_volatility\n",
        "        resid = fixed_fit.resid\n",
        "\n",
        "        resid_lag=shift(resid,1,cval=np.NaN)\n",
        "        resid=resid_lag[1:]\n",
        "        conVol_lag=shift(conVol,1,cval=np.NaN)\n",
        "        conVol=conVol_lag[1:]\n",
        "        r_gen=r_gen[1:]\n",
        "        \n",
        "        m[0]=np.sum(-1/(omega+alpha*np.square(resid)+beta*conVol)+np.divide(np.square(r_gen),2*np.square(omega+alpha*np.square(resid)+beta*conVol)))\n",
        "        m[1]=np.sum(-np.divide(np.square(resid),(omega+alpha*np.square(resid)+beta*conVol))+np.divide(np.multiply(np.square(r_gen),np.square(resid)),2*np.square(omega+alpha*np.square(resid)+beta*conVol)))\n",
        "        m[2]=np.sum(-np.divide(conVol,(omega+alpha*np.square(resid)+beta*conVol))+np.divide(np.multiply(np.square(r_gen),conVol),2*np.square(omega+alpha*np.square(resid)+beta*conVol)))\n",
        "        m=m/N\n",
        "        result=np.matmul(m.T,np.matmul(Omega,m))\n",
        "        return result\n",
        "    \n",
        "    def calibrate_european(self,params):\n",
        "       '''\n",
        "       Second step of heston calibration, calculates kappa, theta and eta\n",
        "       '''\n",
        "        k_1=params[0]\n",
        "        theta_1=params[1]\n",
        "        eta_1=params[2]\n",
        "        #Optimize parameters for every trading day\n",
        "        date_vec=self.option_data_european[\"date\"].to_numpy()\n",
        "        days=len(set(self.option_data_european[\"date\"].to_numpy()))\n",
        "        v_vec=np.zeros([days,1])\n",
        "        rho_vec=np.zeros([days,1])\n",
        "        day_selector=0\n",
        "        \n",
        "        bound=0.999\n",
        "\n",
        "        for day in range(0,days):\n",
        "            if day==10:\n",
        "              print(rho_vec[0:day])\n",
        "            if (day%100==0):\n",
        "              print(\"day: \" + str(day) + \" of \" + str(days-1))\n",
        "              \n",
        "            #Set initial parameters\n",
        "            if day==0:\n",
        "                date=date_vec[day_selector]\n",
        "                v0=0.0349\n",
        "                rho0=-0.487\n",
        "            else:\n",
        "                while (date_vec[day_selector]==prev_date):\n",
        "                    day_selector=day_selector+1\n",
        "                date=date_vec[day_selector]\n",
        "                v0=v_vec[day-1]\n",
        "                rho0=rho_vec[day-1]\n",
        "                if abs(rho0)==bound:\n",
        "                  rho0=-0.487\n",
        "            \n",
        "            #select the correct options\n",
        "            day_data = self.option_data_european[(option_data_european['date']==date)]\n",
        "            #Minimize for these options\n",
        "            res=scipy.optimize.minimize(self.sum_squared_error,x0=[v0,rho0],args=(day_data,k_1,theta_1,eta_1),bounds=((0, 1),(-1*bound,bound)),options={'maxiter': 20})\n",
        "            solution=res.x\n",
        "            v_vec[day]=solution[0]\n",
        "            rho_vec[day]=solution[1]\n",
        "            prev_date=date\n",
        "        \n",
        "        #This solution should be the final parameters v, rho, lamda     \n",
        "        v=np.mean(v_vec)\n",
        "        rho=np.mean(rho_vec)\n",
        "        print(\"table information for v: mean: \" + str(np.mean(v_vec)) + \" median: \" + str(np.median(v_vec)) + \" sd: \" + str(np.std(v_vec)) + \" min: \" + str(min(v_vec)) + \" max: \" + str(max(v_vec)))\n",
        "        print(\"table information for rho: mean: \" + str(np.mean(rho_vec)) + \" median: \" + str(np.median(rho_vec)) + \" sd: \" + str(np.std(rho_vec)) + \" min: \" + str(min(rho_vec)) + \" max: \" + str(max(rho_vec)))\n",
        "        print(\"v: \" + str(v) + \"(0.03) rho: \" + str(rho) + \"(-0.49), numbers in brackets are from AitSahlia\")\n",
        "        return np.array([v,rho])\n",
        "        \n",
        "    def put_price(self,K,x,v,T,r,kappa,theta,eta,lamda,rho):\n",
        "       '''\n",
        "       Calculate put option price using put call parity\n",
        "       '''\n",
        "        call_price=self.calcFFT(x,K,r,T,v,kappa,theta,eta,lamda,rho)\n",
        "        #Use put call parity\n",
        "        return call_price+K*np.exp(-r*T)-x\n",
        "    \n",
        "    def calcFFT(self,x,K,r,T,v,kappa,theta,eta,lamda,rho):\n",
        "      '''\n",
        "      Calculate call price using FFT, adopted code from Financial engineering course\n",
        "      '''\n",
        "        alpha = 4\n",
        "        N=2**12\n",
        "        Upperlimit=1000\n",
        "        etaa=Upperlimit/N\n",
        "        lambdaFFT=(2*np.pi)/(N*etaa)\n",
        "        b=N*lambdaFFT/2\n",
        "        u=np.linspace(0,N-1,N)*etaa\n",
        "        KGrid = -b+lambdaFFT*np.linspace(0,N-1,N)\n",
        "        help_vec=np.zeros([N])\n",
        "        help_vec[0]=1\n",
        "        #Carr-Madan Equation\n",
        "        Psi=np.exp(-r*T)*np.divide(self.HestonCF(u-(alpha+1)*complex(0,1),x,r,T,v,kappa,theta,eta,rho,lamda),(alpha**2+alpha-np.multiply(u,u)+complex(0,1)*(2*alpha+1)*u))\n",
        "        Function=np.multiply(np.exp(complex(0,1)*b*u),np.multiply(Psi,((etaa/3)*(3+np.power(-1,np.linspace(1,N,N))-help_vec))))\n",
        "        FastFourierPriceGrid=(np.exp(-KGrid*alpha)/np.pi)*np.real(np.fft.fft(Function))\n",
        "        SpotOnGrid = (np.log(K)+b)/lambdaFFT+1\n",
        "        return (1-(SpotOnGrid-np.floor(SpotOnGrid)))*FastFourierPriceGrid[int(np.floor(SpotOnGrid))-1]+(SpotOnGrid-np.floor(SpotOnGrid))*FastFourierPriceGrid[int(np.floor(SpotOnGrid))]\n",
        "    \n",
        "    def HestonCF(self,Phi,S0,r,T,V0,kappa,theta,sigma,rho,lamda):\n",
        "      '''\n",
        "      Calculate Heston characteristic function, adopted code from Financial engineering course\n",
        "      '''\n",
        "        a=kappa*theta\n",
        "        u=-0.5\n",
        "        b = kappa+lamda\n",
        "        d=np.sqrt((rho*sigma*complex(0,1)*Phi-b)**2-sigma**2*(2*u*complex(0,1)*Phi-Phi**2))\n",
        "        g=(b-rho*sigma*complex(0,1)*Phi-d)/(b-rho*sigma*complex(0,1)*Phi+d)\n",
        "        D=(b-rho*sigma*complex(0,1)*Phi-d)/(sigma**2*(1-np.exp(-d*T))/(1-g*np.exp(-d*T)))\n",
        "        C=r*complex(0,1)*Phi*T+(a/(sigma**2))*((b-rho*sigma*complex(0,1)*Phi-d)*T-2*np.log(((1-g*np.exp(-d*T))/(1-g))))            \n",
        "        return_value=np.exp(C+D*V0+complex(0,1)*Phi*np.log(S0))\n",
        "        return return_value\n",
        "    \n",
        "    #function that defines optimization criterium\n",
        "    def sum_squared_error(self,params,day_data,kappa,theta,eta):\n",
        "      '''\n",
        "      Calculate sum of squared errors, which is used as an optimization criterium\n",
        "      '''\n",
        "        #print('calculating SSE')\n",
        "        v=params[0]\n",
        "        rho=params[1]\n",
        "        lamda=0\n",
        "        SSE=0\n",
        "        for index, row in day_data.iterrows():\n",
        "            real_price=row['market price']\n",
        "            estimated_price=self.put_price(row['strike_price'],row['underlying'],v,row['maturity'],0,kappa,theta,eta,lamda,rho)\n",
        "            SSE=SSE+(real_price-estimated_price)**2\n",
        "        if (math.isnan(SSE)):\n",
        "            SSE=10**20\n",
        "        return SSE\n",
        "    \n",
        "    def calibrate(self):\n",
        "      '''\n",
        "      Wrapper function for all calibration\n",
        "      '''\n",
        "        print(\"Calibrating structural parameters\")\n",
        "        Theta1=self.calibrate_structural()\n",
        "        print(\"Calibrating on European options\")\n",
        "        Par=self.calibrate_european(Theta1)\n",
        "        Params=np.array([Theta1[0],Theta1[1],Theta1[2],Par[0],Par[1]])\n",
        "        print(Params)\n",
        "        return Params\n",
        "    \n",
        "    #Laguerre polynomials\n",
        "    def L0(self,X):\n",
        "      '''\n",
        "      Laguerre polynomial 0\n",
        "      '''\n",
        "        return np.exp(-X/2)\n",
        "    def L1(self,X):\n",
        "      '''\n",
        "      Laguerre polynomial 1\n",
        "      '''\n",
        "        return np.multiply(np.exp(-X/2),(1-X))\n",
        "    def L2(self,X):\n",
        "      '''\n",
        "      Laguerre polynomial 2\n",
        "      '''\n",
        "        return (1/2)*np.multiply(np.exp(-X/2),(np.multiply(X,X)-4*X+2))\n",
        "    \n",
        "    def generate_Heston_matrix(self,v_0,rho,kappa,theta,eta,m,N,S_0,h,epsilon):\n",
        "      '''\n",
        "      Generate heston data, which is vectorized as far as possible (hard to do due to the time dependence)\n",
        "      '''\n",
        "        S_paths=np.zeros([N,m])\n",
        "        #Multiply epsilon by h to deal with the timestep\n",
        "        epsilon=epsilon*np.sqrt(h)\n",
        "        v_0=v_0*np.ones([1,N])\n",
        "        for ti in range(0,m):\n",
        "            if ti==0:\n",
        "                v=kappa*theta+(1-kappa)*v_0+eta*np.sqrt(v_0)*epsilon[ti,:,1]\n",
        "                v=abs(v)\n",
        "                S=np.exp(np.multiply(np.sqrt(v),epsilon[ti,:,0]))*S_0\n",
        "                S_paths[:,ti]=S\n",
        "            else:\n",
        "                v=kappa*theta+(1-kappa)*v+eta*np.sqrt(v)*epsilon[ti,:,1]\n",
        "                v=abs(v)\n",
        "                S=np.exp(np.multiply(np.sqrt(v),epsilon[ti,:,0]))*S_0\n",
        "                S_paths[:,ti]=S\n",
        "        return S_paths\n",
        "    \n",
        "    def price_option_LSM(self,S_0,K,maturity,r,epsilon,params,m,N):\n",
        "      '''\n",
        "      Price options with Heston using the least squares Monte Carlo algorithm by Longstaff and Schwartz\n",
        "      '''\n",
        "        kappa=params[0]\n",
        "        theta=params[1]\n",
        "        eta=params[2]\n",
        "        v=params[3]\n",
        "        rho=params[4]\n",
        "        h=maturity/m\n",
        "        max_vec=np.vectorize(max,otypes=[np.float64])\n",
        "        #simulate path\n",
        "        S_paths=self.generate_Heston_matrix(v,rho,kappa,theta,eta,m,N,S_0,h,epsilon)\n",
        "       \n",
        "        #create matrix of cashflows, and matrix of discount rates\n",
        "        cashflow_matrix=np.zeros([N,m])\n",
        "        discount_matrix=np.ones([N,m])\n",
        "        for ti in range(0,m):\n",
        "            discount_matrix[:,ti]=discount_matrix[:,ti]*np.exp(-r*ti)    \n",
        "        cashflow_matrix[:,m-1]=max_vec(K-S_paths[:,m-1],0)\n",
        "    \n",
        "        #recursively calculate the cashflows\n",
        "        for ti in range(m-2,-1,-1):\n",
        "            exercise_value=max_vec(K-S_paths[:,ti],0)\n",
        "            #calculate continuation value by regressing in the money options\n",
        "            itm_indices=np.where(exercise_value > 0)[0]\n",
        "            if (np.shape(itm_indices)[0]>0):\n",
        "              Y=np.matmul(np.multiply(cashflow_matrix,discount_matrix),np.ones([m,1]))\n",
        "              X=np.column_stack([np.ones([N,1]),self.L0(S_paths[:,ti]),self.L1(S_paths[:,ti]),self.L2(S_paths[:,ti])])\n",
        "              Y_itm=Y[itm_indices]\n",
        "              X_itm=X[itm_indices,:] \n",
        "              beta=np.linalg.lstsq(np.matmul(X_itm.T,X_itm),np.matmul(X_itm.T,Y_itm),rcond=1)[0]\n",
        "              continuation_value=np.matmul(X,beta)\n",
        "              exercise_indices=np.where((exercise_value>continuation_value[0,:])*1 == 1)[0]\n",
        "              cashflow_matrix[exercise_indices,:]=np.zeros([len(exercise_indices),m])\n",
        "              cashflow_matrix[exercise_indices,ti]=exercise_value[exercise_indices]\n",
        "        #the option price is the mean of the discounted cashflows\n",
        "        option_value=np.mean(np.matmul(np.multiply(cashflow_matrix,discount_matrix),np.ones([m,1])))\n",
        "        return option_value\n",
        "    \n",
        "    def price_american_options(self,option_data,params,m=50,N=1000):\n",
        "      '''\n",
        "      Function that does the option pricing, using the price_option_LSM function\n",
        "      '''\n",
        "        rho=params[4]\n",
        "        epsilon=np.random.multivariate_normal([0,0],[[1,rho],[rho,1]],[m,N])\n",
        "        i=0\n",
        "        mape=0\n",
        "        mse=0\n",
        "        rows=np.shape(option_data)[0]\n",
        "        predicted_prices=np.zeros(rows)\n",
        "        total_time=0\n",
        "        #rows=1000\n",
        "        for index, row in option_data.iterrows():          \n",
        "              if (i%np.round(rows/10)==0):\n",
        "                print(i)\n",
        "              if i>rows:\n",
        "                break\n",
        "              start_price_time=time.perf_counter() \n",
        "              estimated_option_value=self.price_option_LSM(row[\"underlying\"],row[\"strike_price\"],row[\"maturity\"],row[\"interest_rate\"]/250,epsilon,params,m,N)\n",
        "              predicted_prices[i]=estimated_option_value\n",
        "              end_price_time=time.perf_counter() \n",
        "              total_time=total_time+end_price_time-start_price_time\n",
        "              true_option_value=row[\"market price\"]\n",
        "              mape=mape+(1/rows)*(np.abs(estimated_option_value-true_option_value)/true_option_value)\n",
        "              mse=mse+(1/rows)*(true_option_value-estimated_option_value)**2\n",
        "              i=i+1\n",
        "        print(\"MAPE: \" + str(mape))\n",
        "        print(\"RMSE: \" + str(np.sqrt(mse)))\n",
        "        print(\"total time: \" + str(total_time) + \", time per option: \" + str(total_time/rows))\n",
        "        return predicted_prices"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "y-oHa9iqBAtr"
      },
      "source": [
        "Heston = HestonModel(option_data_european,underlying_data)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "sCK3jyO6BdBt",
        "outputId": "afb10a33-acac-4073-af9d-aba6031e5c9d"
      },
      "source": [
        "params = Heston.calibrate()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Calibrating structural parameters\n",
            "for Gamma0: omega: 0.022698678972389693(3*10^-7) alpha: 0.12181926048482378(0.04) beta: 0.8599105317370401(0.95), numbers in brackets are from AitSahlia\n",
            "for Theta0: kappa: 1.2423875660326757(0.0044) theta: 0.01827020777813604(6.93*10^-5) eta: 0.2772924072529605(0.0653), numbers in brackets are from AitSahlia\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/arch/univariate/base.py:317: DataScaleWarning: y is poorly scaled, which may affect convergence of the optimizer when\n",
            "estimating the model parameters. The scale of y is 0.04389. Parameter\n",
            "estimation work better when this value is between 1 and 1000. The recommended\n",
            "rescaling is 10 * y.\n",
            "\n",
            "This warning can be disabled by either rescaling y before initializing the\n",
            "model or by setting rescale=False.\n",
            "\n",
            "  data_scale_warning.format(orig_scale, rescale), DataScaleWarning\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "for Gamma1: omega: 0.03517553983599765(4*10^-9) alpha: 0.12450676040371353(0.45) beta: 0.07605799554762208(0.55), numbers in brackets are from AitSahlia\n",
            "Final solution=Theta1: kappa: 1.2010669234372058(2.65) theta: 0.08867374916911482(0.029) eta: 0.3213213814947314(0.154), numbers in brackets are from AitSahlia\n",
            "Calibrating on European options\n",
            "day: 0 of 2514\n",
            "[[ 0.05099928]\n",
            " [-0.5557435 ]\n",
            " [-0.52872383]\n",
            " [-0.40503286]\n",
            " [-0.40503286]\n",
            " [-0.03850996]\n",
            " [-0.31544644]\n",
            " [-0.48502061]\n",
            " [ 0.00283801]\n",
            " [-0.03642785]]\n",
            "day: 100 of 2514\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/numpy/core/_asarray.py:83: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray\n",
            "  return array(a, dtype, copy=False, order=order)\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "day: 200 of 2514\n",
            "day: 300 of 2514\n",
            "day: 400 of 2514\n",
            "day: 500 of 2514\n",
            "day: 600 of 2514\n",
            "day: 700 of 2514\n",
            "day: 800 of 2514\n",
            "day: 900 of 2514\n",
            "day: 1000 of 2514\n",
            "day: 1100 of 2514\n",
            "day: 1200 of 2514\n",
            "day: 1300 of 2514\n",
            "day: 1400 of 2514\n",
            "day: 1500 of 2514\n",
            "day: 1600 of 2514\n",
            "day: 1700 of 2514\n",
            "day: 1800 of 2514\n",
            "day: 1900 of 2514\n",
            "day: 2000 of 2514\n",
            "day: 2100 of 2514\n",
            "day: 2200 of 2514\n",
            "day: 2300 of 2514\n",
            "day: 2400 of 2514\n",
            "day: 2500 of 2514\n",
            "table information for v: mean: 0.0011282141384564395 median: 0.0006185032044494491 sd: 0.0016731911414877385 min: [-6.77626358e-21] max: [0.01745646]\n",
            "table information for rho: mean: -0.23905062750652212 median: -0.11851606658145211 sd: 0.35581706914939054 min: [-0.999] max: [0.999]\n",
            "v: 0.0011282141384564395(0.03) rho: -0.23905062750652212(-0.49), numbers in brackets are from AitSahlia\n",
            "[ 1.20106692e+00  8.86737492e-02  3.21321381e-01  1.12821414e-03\n",
            " -2.39050628e-01]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 772
        },
        "id": "OEzh3vASBcvN",
        "outputId": "3d2af9f1-0cef-4d56-ee5d-d438b3ba5ca6"
      },
      "source": [
        "params=np.array([ 1.20106692e+00,  8.86737492e-02,  3.21321381e-01,  1.12821414e-03, -2.39050628e-01])\n",
        "predicted_prices=[]\n",
        "\n",
        "\n",
        "for i in range(0,3):\n",
        "  if i==0:\n",
        "    period='pre-crisis'\n",
        "  if i==1:\n",
        "    period='crisis'\n",
        "  if i==2:\n",
        "    period='post-crisis'\n",
        "  if period == 'pre-crisis':\n",
        "    data = option_data[(option_data['date'] >= pd.Timestamp(2003,1,1)) & (option_data['date'] < pd.Timestamp(2007,1,1))]\n",
        "  elif period == 'crisis':\n",
        "    data = option_data[(option_data['date'] >= pd.Timestamp(2007,1,1)) & (option_data['date'] < pd.Timestamp(2010,1,1))]\n",
        "  elif period == 'post-crisis':\n",
        "    data = option_data[(option_data['date'] >= pd.Timestamp(2010,1,1)) & (option_data['date'] < pd.Timestamp(2013,1,1))]\n",
        "  else:\n",
        "    raise ValueError('Not a valid string for period')\n",
        "\n",
        "  print(period)\n",
        "  prices=Heston.price_american_options(data,params)\n",
        "  predicted_prices=np.hstack((predicted_prices,prices))\n",
        "\n",
        "savetxt('heston_prediction.csv', predicted_prices, delimiter=',')\n",
        "files.download(\"heston_prediction.csv\")\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "pre-crisis\n",
            "0\n",
            "3504\n",
            "7008\n",
            "10512\n",
            "14016\n",
            "17520\n",
            "21024\n",
            "24528\n",
            "28032\n",
            "31536\n",
            "MAPE: 0.7329983272246912\n",
            "RMSE: 4.91708388202715\n",
            "total time: 1461.707709550912, time per option: 0.04171659321187569\n",
            "crisis\n",
            "0\n",
            "3670\n",
            "7340\n",
            "11010\n",
            "14680\n",
            "18350\n",
            "22020\n",
            "25690\n",
            "29360\n",
            "33030\n",
            "MAPE: 0.6938676632478358\n",
            "RMSE: 6.548476150446655\n",
            "total time: 1443.8746176392833, time per option: 0.039344776762746836\n",
            "post-crisis\n",
            "0\n",
            "3176\n",
            "6352\n",
            "9528\n",
            "12704\n",
            "15880\n",
            "19056\n",
            "22232\n",
            "25408\n",
            "28584\n",
            "MAPE: 0.7390427384784961\n",
            "RMSE: 6.041260037677221\n",
            "total time: 1224.3494190569818, time per option: 0.03855125851119311\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "application/javascript": [
              "\n",
              "    async function download(id, filename, size) {\n",
              "      if (!google.colab.kernel.accessAllowed) {\n",
              "        return;\n",
              "      }\n",
              "      const div = document.createElement('div');\n",
              "      const label = document.createElement('label');\n",
              "      label.textContent = `Downloading \"${filename}\": `;\n",
              "      div.appendChild(label);\n",
              "      const progress = document.createElement('progress');\n",
              "      progress.max = size;\n",
              "      div.appendChild(progress);\n",
              "      document.body.appendChild(div);\n",
              "\n",
              "      const buffers = [];\n",
              "      let downloaded = 0;\n",
              "\n",
              "      const channel = await google.colab.kernel.comms.open(id);\n",
              "      // Send a message to notify the kernel that we're ready.\n",
              "      channel.send({})\n",
              "\n",
              "      for await (const message of channel.messages) {\n",
              "        // Send a message to notify the kernel that we're ready.\n",
              "        channel.send({})\n",
              "        if (message.buffers) {\n",
              "          for (const buffer of message.buffers) {\n",
              "            buffers.push(buffer);\n",
              "            downloaded += buffer.byteLength;\n",
              "            progress.value = downloaded;\n",
              "          }\n",
              "        }\n",
              "      }\n",
              "      const blob = new Blob(buffers, {type: 'application/binary'});\n",
              "      const a = document.createElement('a');\n",
              "      a.href = window.URL.createObjectURL(blob);\n",
              "      a.download = filename;\n",
              "      div.appendChild(a);\n",
              "      a.click();\n",
              "      div.remove();\n",
              "    }\n",
              "  "
            ],
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "application/javascript": [
              "download(\"download_92231de8-50dc-4edf-bcd5-592bc7affc5d\", \"heston_prediction.csv\", 2587400)"
            ],
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cxaWyQYy_EAy"
      },
      "source": [
        "# ad-hoc Black-Scholes (AH-BS)\n",
        "\n",
        "This contains the steps seperately for testing, the full object oriented, commented code is in Class ad-hoc black scholes\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "qfEcKOPx_S4q",
        "outputId": "5daaea86-a482-456a-e8aa-1904e6bc93b4"
      },
      "source": [
        "max_vec=np.vectorize(max, otypes=[np.float64])\n",
        "\n",
        "def create_regression_data(X):\n",
        "  X_reg = X[['strike_price','maturity']]\n",
        "  X_reg['KT']=(X_reg['strike_price']*X_reg['maturity'])\n",
        "  X_reg=X_reg.values\n",
        "  return X_reg\n",
        "\n",
        "def implied_volatility(data):\n",
        "  underlying = data[['underlying']].values.ravel().astype(float)\n",
        "  strike_price = data[['strike_price']].values.ravel().astype(float)\n",
        "  maturity = data[['maturity']].values.ravel().astype(float)\n",
        "  interest_rate = data[['interest_rate']].values.ravel().astype(float)/250\n",
        "  #interest_rate = interest_rate*0\n",
        "  value = data[['market price']].values.ravel().astype(float)\n",
        "  return find_vol(value,interest_rate,underlying,maturity,strike_price)\n",
        "\n",
        "def calculate_prices(vol,data):\n",
        "  underlying = data[['underlying']].values.ravel().astype(float)\n",
        "  strike_price = data[['strike_price']].values.ravel().astype(float)\n",
        "  maturity = data[['maturity']].values.ravel().astype(float)\n",
        "  interest_rate = data[['interest_rate']].values.ravel().astype(float)/250\n",
        "  #interest_rate = interest_rate*0\n",
        "  #return bs_formula_P(interest_rate,vol,underlying,maturity,strike_price)\n",
        "  return max_vec(bs_formula_P(interest_rate,vol,underlying,maturity,strike_price),0)\n",
        "\n",
        "def find_vol(V,r,s,T,K):\n",
        "    if isinstance(V, float):\n",
        "        x0=np.ones(1)*0.5\n",
        "    else:\n",
        "        x0=np.ones(len(V))*0.5\n",
        "    tol=10**-5\n",
        "    f = lambda sigma: bs_formula_P(r,sigma,s,T,K)-V\n",
        "    df = lambda sigma: vega(r,sigma,s,T,K)\n",
        "    return newton(f,df,x0,tol)\n",
        "\n",
        "def bs_formula_P(r,sigma,s,t,K):\n",
        "    # Value of an European put option\n",
        "    d1 = np.log(np.divide(s,K)) + np.divide(np.multiply((0.5*np.square(sigma)+r),t),np.multiply(sigma,np.sqrt(t)))\n",
        "    d2 = d1 - np.multiply(sigma,np.sqrt(t))\n",
        "    P = np.multiply(-s,norm.cdf(-d1)) + np.multiply(np.multiply(K,np.exp(np.multiply(-r,t))),norm.cdf(-d2))\n",
        "    return P\n",
        "\n",
        "def vega(r,sigma,s,t,K):\n",
        "    d1 = np.log(np.divide(s,K)) + np.divide(np.multiply((0.5*np.square(sigma)+r),t),np.multiply(sigma,np.sqrt(t)))\n",
        "    return np.multiply(np.multiply(s,norm.pdf(d1)),np.sqrt(t))\n",
        "\n",
        "def newton(f,df,x0,tol):\n",
        "    x = x0\n",
        "    maxit = 100\n",
        "    it = 0\n",
        "    ind = np.abs(f(x)/df(x))>tol\n",
        "    while it < maxit and np.any(ind):\n",
        "        # Iterate on the indices that haven't yet converged\n",
        "        ind = np.abs(f(x)/df(x))>tol\n",
        "        x[ind]=x[ind]-np.divide(f(x),df(x))[ind]\n",
        "        it=it+1\n",
        "        # new set of indices to iterate on\n",
        "    if np.any(ind):\n",
        "        print('Warning: newton did not converge')\n",
        "    else:\n",
        "        print('converged in {it} iterations'.format(it = it))\n",
        "    return x\n",
        "\n",
        "#This array will have all prices obtained from the\n",
        "predicted_prices_all=[]\n",
        "predicted_prices_in_and_out=[]\n",
        "\n",
        "for i in range(0,3):\n",
        "  if i==0:\n",
        "    period='pre-crisis'\n",
        "  if i==1:\n",
        "    period='crisis'\n",
        "  if i==2:\n",
        "    period='post-crisis'\n",
        "  if period == 'pre-crisis':\n",
        "    train = option_data[(option_data['date'] >= pd.Timestamp(2003,1,1)) & (option_data['date'] < pd.Timestamp(2006,7,1))]\n",
        "    test = option_data[(option_data['date'] >= pd.Timestamp(2006,7,1)) & (option_data['date'] < pd.Timestamp(2007,1,1))]\n",
        "  elif period == 'crisis':\n",
        "    train = option_data[(option_data['date'] >= pd.Timestamp(2007,1,1)) & (option_data['date'] < pd.Timestamp(2009,7,1))]\n",
        "    test = option_data[(option_data['date'] >= pd.Timestamp(2009,7,1)) & (option_data['date'] < pd.Timestamp(2010,1,1))]\n",
        "  elif period == 'post-crisis':\n",
        "    train = option_data[(option_data['date'] >= pd.Timestamp(2010,1,1)) & (option_data['date'] < pd.Timestamp(2012,7,1))]\n",
        "    test = option_data[(option_data['date'] >= pd.Timestamp(2012,7,1)) & (option_data['date'] < pd.Timestamp(2013,1,1))]\n",
        "  else:\n",
        "    raise ValueError('Not a valid string for period')\n",
        "\n",
        "  start_time=time.perf_counter()\n",
        "\n",
        "  #Estimate the regression on train data\n",
        "  impl_vol=implied_volatility(train)\n",
        "  if i==0:\n",
        "    training_data_pred=train\n",
        "  else:\n",
        "    training_data_pred=pd.concat((training_data_pred,train))\n",
        "  X_reg = create_regression_data(train)\n",
        "  y_true = train[['market price']].values.ravel()\n",
        "  linreg = LinearRegression().fit(X_reg, impl_vol)\n",
        "\n",
        "  #Add predicted prices to the vector of predicted prices (this can be ignored)\n",
        "  vol_reg = linreg.predict(X_reg)\n",
        "  y_reg = calculate_prices(vol_reg,train)\n",
        "  if i==0:\n",
        "    predicted_prices_in_and_out=np.hstack((predicted_prices_in_and_out,y_reg))\n",
        "  else:\n",
        "    predicted_prices_in_and_out=np.hstack((predicted_prices_in_and_out,np.zeros(len(training_data_pred)-len(predicted_prices_in_and_out))))\n",
        "  training_data_pred=pd.concat((training_data_pred,test))\n",
        "\n",
        "  #Predict test data using the estimated regression\n",
        "  X_reg_pred = create_regression_data(test)\n",
        "  vol_pred = linreg.predict(X_reg_pred)\n",
        "  y_pred = calculate_prices(vol_pred,test)\n",
        "  predicted_prices_in_and_out=np.hstack((predicted_prices_in_and_out,y_pred)) \n",
        "  y2 = test[['market price']].values.ravel()\n",
        "\n",
        "  #Estimate on all data to get estimation errors\n",
        "  if i==0:\n",
        "    training_data=pd.concat((train,test))\n",
        "  else:\n",
        "    training_data=pd.concat((training_data,train,test))\n",
        "  estimation_data=pd.concat((train,test))\n",
        "  impl_vol=implied_volatility(training_data)\n",
        "  X_reg_est = create_regression_data(training_data)\n",
        "  linreg = LinearRegression().fit(X_reg_est, impl_vol)\n",
        "  X_reg_est = create_regression_data(estimation_data)\n",
        "  vol_est = linreg.predict(X_reg_est)\n",
        "  y_est = calculate_prices(vol_est,estimation_data)\n",
        "  y = estimation_data[['market price']].values.ravel()\n",
        "  predicted_prices_all=np.hstack((predicted_prices_all,y_est))\n",
        "\n",
        "  #Plot results\n",
        "  #plt.figure(i)\n",
        "  #plt.scatter(impl_vol,vol_est)\n",
        "  #plt.plot([0, 1], [0, 1], color = 'black', linewidth = 2)\n",
        "  #plt.xlabel('impl vol')\n",
        "  #plt.ylabel('reg vol')\n",
        "  #plt.figure(i+3)\n",
        "  #plt.scatter(y,calculate_prices(impl_vol,estimation_data),c='g')\n",
        "  #plt.scatter(y,y_est,c='r')\n",
        "  #plt.xlabel('true price')\n",
        "  #plt.ylabel('model')\n",
        "\n",
        "  end_time=time.perf_counter()\n",
        "\n",
        "  #Calculate and print errors\n",
        "  mape_in=np.mean(np.divide(np.abs(y_est-y),y))\n",
        "  print(y[0:10])\n",
        "  print(y_est[0:10])\n",
        "  rmse_in=np.sqrt(np.mean((((y_est-y)**2))))\n",
        "  mape_out=np.mean(np.divide(np.abs(y_pred-y2),y2))\n",
        "  rmse_out=np.sqrt(np.mean((((y_pred-y2)**2))))\n",
        "\n",
        "  print(period + \" MAPE AH-BS in sample: \" + str(mape_in))\n",
        "  print(period + \" RMSE AH-BS in sample: \" + str(rmse_in))\n",
        "  print(period + \" MAPE AH-BS out sample: \" + str(mape_out))\n",
        "  print(period + \" RMSE AH-BS out sample: \" + str(rmse_out))\n",
        "  print(\"time \" + str(end_time-start_time))\n",
        "\n",
        "savetxt('ahbs_estimation.csv', predicted_prices_all, delimiter=',')\n",
        "files.download(\"ahbs_estimation.csv\")\n",
        "savetxt('ahbs_prediction.csv', predicted_prices_in_and_out, delimiter=',')\n",
        "files.download(\"ahbs_prediction.csv\")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "converged in 7 iterations\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:5: SettingWithCopyWarning: \n",
            "A value is trying to be set on a copy of a slice from a DataFrame.\n",
            "Try using .loc[row_indexer,col_indexer] = value instead\n",
            "\n",
            "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
            "  \"\"\"\n",
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:5: SettingWithCopyWarning: \n",
            "A value is trying to be set on a copy of a slice from a DataFrame.\n",
            "Try using .loc[row_indexer,col_indexer] = value instead\n",
            "\n",
            "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
            "  \"\"\"\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "converged in 7 iterations\n",
            "[42.05   0.125  0.7    1.25   1.65   2.15   3.25   1.075  1.85   2.675]\n",
            "[35.34393316  0.          0.          0.          0.          0.\n",
            "  2.42338098  0.          0.          0.        ]\n",
            "pre-crisis MAPE AH-BS in sample: 0.7646752590209573\n",
            "pre-crisis RMSE AH-BS in sample: 4.248797278999317\n",
            "pre-crisis MAPE AH-BS out sample: 0.7793734331615575\n",
            "pre-crisis RMSE AH-BS out sample: 4.930745551292388\n",
            "time 0.6870655530000249\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:5: SettingWithCopyWarning: \n",
            "A value is trying to be set on a copy of a slice from a DataFrame.\n",
            "Try using .loc[row_indexer,col_indexer] = value instead\n",
            "\n",
            "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
            "  \"\"\"\n",
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:5: SettingWithCopyWarning: \n",
            "A value is trying to be set on a copy of a slice from a DataFrame.\n",
            "Try using .loc[row_indexer,col_indexer] = value instead\n",
            "\n",
            "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
            "  \"\"\"\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "converged in 9 iterations\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:5: SettingWithCopyWarning: \n",
            "A value is trying to be set on a copy of a slice from a DataFrame.\n",
            "Try using .loc[row_indexer,col_indexer] = value instead\n",
            "\n",
            "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
            "  \"\"\"\n",
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:5: SettingWithCopyWarning: \n",
            "A value is trying to be set on a copy of a slice from a DataFrame.\n",
            "Try using .loc[row_indexer,col_indexer] = value instead\n",
            "\n",
            "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
            "  \"\"\"\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "converged in 9 iterations\n",
            "[0.575 0.875 1.125 0.35  0.55  0.775 1.05  1.6   2.45  3.35 ]\n",
            "[0.         0.         0.         0.         0.         0.\n",
            " 1.77705596 3.69074974 5.62650919 7.58345773]\n",
            "crisis MAPE AH-BS in sample: 0.7175807276501289\n",
            "crisis RMSE AH-BS in sample: 8.796895523421066\n",
            "crisis MAPE AH-BS out sample: 2.3268557415817144\n",
            "crisis RMSE AH-BS out sample: 13.618105630059121\n",
            "time 0.99386025900003\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:5: SettingWithCopyWarning: \n",
            "A value is trying to be set on a copy of a slice from a DataFrame.\n",
            "Try using .loc[row_indexer,col_indexer] = value instead\n",
            "\n",
            "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
            "  \"\"\"\n",
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:5: SettingWithCopyWarning: \n",
            "A value is trying to be set on a copy of a slice from a DataFrame.\n",
            "Try using .loc[row_indexer,col_indexer] = value instead\n",
            "\n",
            "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
            "  \"\"\"\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "converged in 7 iterations\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:5: SettingWithCopyWarning: \n",
            "A value is trying to be set on a copy of a slice from a DataFrame.\n",
            "Try using .loc[row_indexer,col_indexer] = value instead\n",
            "\n",
            "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
            "  \"\"\"\n",
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:5: SettingWithCopyWarning: \n",
            "A value is trying to be set on a copy of a slice from a DataFrame.\n",
            "Try using .loc[row_indexer,col_indexer] = value instead\n",
            "\n",
            "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
            "  \"\"\"\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "converged in 9 iterations\n",
            "[ 1.6    2.175  3.2    4.95   7.35  10.5    1.125  7.4    8.75  10.4  ]\n",
            "[ 8.39859627 10.5215203  12.67880771 14.87002018 17.09472381 19.35248907\n",
            "  6.31047831 19.49916964 21.47014363 23.47214495]\n",
            "post-crisis MAPE AH-BS in sample: 0.8140862169168339\n",
            "post-crisis RMSE AH-BS in sample: 5.5349319335698715\n",
            "post-crisis MAPE AH-BS out sample: 0.7961448688855137\n",
            "post-crisis RMSE AH-BS out sample: 7.563748146964185\n",
            "time 1.1906699439999784\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:5: SettingWithCopyWarning: \n",
            "A value is trying to be set on a copy of a slice from a DataFrame.\n",
            "Try using .loc[row_indexer,col_indexer] = value instead\n",
            "\n",
            "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
            "  \"\"\"\n",
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:5: SettingWithCopyWarning: \n",
            "A value is trying to be set on a copy of a slice from a DataFrame.\n",
            "Try using .loc[row_indexer,col_indexer] = value instead\n",
            "\n",
            "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
            "  \"\"\"\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "application/javascript": [
              "\n",
              "    async function download(id, filename, size) {\n",
              "      if (!google.colab.kernel.accessAllowed) {\n",
              "        return;\n",
              "      }\n",
              "      const div = document.createElement('div');\n",
              "      const label = document.createElement('label');\n",
              "      label.textContent = `Downloading \"${filename}\": `;\n",
              "      div.appendChild(label);\n",
              "      const progress = document.createElement('progress');\n",
              "      progress.max = size;\n",
              "      div.appendChild(progress);\n",
              "      document.body.appendChild(div);\n",
              "\n",
              "      const buffers = [];\n",
              "      let downloaded = 0;\n",
              "\n",
              "      const channel = await google.colab.kernel.comms.open(id);\n",
              "      // Send a message to notify the kernel that we're ready.\n",
              "      channel.send({})\n",
              "\n",
              "      for await (const message of channel.messages) {\n",
              "        // Send a message to notify the kernel that we're ready.\n",
              "        channel.send({})\n",
              "        if (message.buffers) {\n",
              "          for (const buffer of message.buffers) {\n",
              "            buffers.push(buffer);\n",
              "            downloaded += buffer.byteLength;\n",
              "            progress.value = downloaded;\n",
              "          }\n",
              "        }\n",
              "      }\n",
              "      const blob = new Blob(buffers, {type: 'application/binary'});\n",
              "      const a = document.createElement('a');\n",
              "      a.href = window.URL.createObjectURL(blob);\n",
              "      a.download = filename;\n",
              "      div.appendChild(a);\n",
              "      a.click();\n",
              "      div.remove();\n",
              "    }\n",
              "  "
            ],
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "application/javascript": [
              "download(\"download_efb06455-b147-43d1-9e2f-5ce4c06369a5\", \"ahbs_estimation.csv\", 2587400)"
            ],
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "application/javascript": [
              "\n",
              "    async function download(id, filename, size) {\n",
              "      if (!google.colab.kernel.accessAllowed) {\n",
              "        return;\n",
              "      }\n",
              "      const div = document.createElement('div');\n",
              "      const label = document.createElement('label');\n",
              "      label.textContent = `Downloading \"${filename}\": `;\n",
              "      div.appendChild(label);\n",
              "      const progress = document.createElement('progress');\n",
              "      progress.max = size;\n",
              "      div.appendChild(progress);\n",
              "      document.body.appendChild(div);\n",
              "\n",
              "      const buffers = [];\n",
              "      let downloaded = 0;\n",
              "\n",
              "      const channel = await google.colab.kernel.comms.open(id);\n",
              "      // Send a message to notify the kernel that we're ready.\n",
              "      channel.send({})\n",
              "\n",
              "      for await (const message of channel.messages) {\n",
              "        // Send a message to notify the kernel that we're ready.\n",
              "        channel.send({})\n",
              "        if (message.buffers) {\n",
              "          for (const buffer of message.buffers) {\n",
              "            buffers.push(buffer);\n",
              "            downloaded += buffer.byteLength;\n",
              "            progress.value = downloaded;\n",
              "          }\n",
              "        }\n",
              "      }\n",
              "      const blob = new Blob(buffers, {type: 'application/binary'});\n",
              "      const a = document.createElement('a');\n",
              "      a.href = window.URL.createObjectURL(blob);\n",
              "      a.download = filename;\n",
              "      div.appendChild(a);\n",
              "      a.click();\n",
              "      div.remove();\n",
              "    }\n",
              "  "
            ],
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "application/javascript": [
              "download(\"download_f38ec58c-7717-40aa-9207-fc9965a49706\", \"ahbs_prediction.csv\", 2587400)"
            ],
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1iaONVshh7X6"
      },
      "source": [
        "#Class ad-hoc black scholes"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QZ5Tma_HeuY2"
      },
      "source": [
        "class AdHocBlackScholes():\n",
        "\n",
        "  def __init__(self,\n",
        "               training_data):\n",
        "    impl_vol = self.implied_volatility(training_data)\n",
        "    X_reg = self.create_regression_data(training_data)\n",
        "    self.linreg = LinearRegression().fit(X_reg, impl_vol)\n",
        "    self.max_vec = np.vectorize(max, otypes=[np.float64])     \n",
        "\n",
        "  def create_regression_data(self,X):\n",
        "    '''\n",
        "    Picks up the correct data for regression\n",
        "    '''\n",
        "    X_reg = X[['strike_price','maturity']]\n",
        "    X_reg['KT']=(X_reg['strike_price']*X_reg['maturity'])\n",
        "    X_reg=X_reg.values\n",
        "    return X_reg\n",
        "\n",
        "  def implied_volatility(self,data):\n",
        "    '''\n",
        "    Process data to and passes it to implied volatility calculator\n",
        "    '''\n",
        "    underlying = data[['underlying']].values.ravel().astype(float)\n",
        "    strike_price = data[['strike_price']].values.ravel().astype(float)\n",
        "    maturity = data[['maturity']].values.ravel().astype(float)\n",
        "    interest_rate = data[['interest_rate']].values.ravel().astype(float)/250\n",
        "    #interest_rate = interest_rate*0\n",
        "    value = data[['market price']].values.ravel().astype(float)\n",
        "    return self.find_vol(value,interest_rate,underlying,maturity,strike_price)\n",
        "\n",
        "  def calculate_prices(self,vol,data):\n",
        "    '''\n",
        "    Calculates option prices using the AH_BS algorithm\n",
        "    '''\n",
        "    underlying = data[['underlying']].values.ravel().astype(float)\n",
        "    strike_price = data[['strike_price']].values.ravel().astype(float)\n",
        "    maturity = data[['maturity']].values.ravel().astype(float)\n",
        "    interest_rate = data[['interest_rate']].values.ravel().astype(float)/250\n",
        "    return self.max_vec(self.bs_formula_P(interest_rate,vol,underlying,maturity,strike_price),0)\n",
        "\n",
        "  def find_vol(self,V,r,s,T,K):\n",
        "    '''\n",
        "    Calculates implied vol, using newton's method\n",
        "    '''\n",
        "      if isinstance(V, float):\n",
        "          x0=np.ones(1)*0.5\n",
        "      else:\n",
        "          x0=np.ones(len(V))*0.5\n",
        "      tol=10**-5\n",
        "      f = lambda sigma: self.bs_formula_P(r,sigma,s,T,K)-V\n",
        "      df = lambda sigma: self.vega(r,sigma,s,T,K)\n",
        "      return self.newton(f,df,x0,tol)\n",
        "\n",
        "  def bs_formula_P(self,r,sigma,s,t,K):\n",
        "    '''\n",
        "    Black-Scholes formula for put option\n",
        "    '''\n",
        "      # Value of an European put option\n",
        "      d1 = np.log(np.divide(s,K)) + np.divide(np.multiply((0.5*np.square(sigma)+r),t),np.multiply(sigma,np.sqrt(t)))\n",
        "      d2 = d1 - np.multiply(sigma,np.sqrt(t))\n",
        "      P = np.multiply(-s,norm.cdf(-d1)) + np.multiply(np.multiply(K,np.exp(np.multiply(-r,t))),norm.cdf(-d2))\n",
        "      return P\n",
        "\n",
        "  def vega(self,r,sigma,s,t,K):\n",
        "    '''\n",
        "    Black-Scholees vega\n",
        "    '''\n",
        "      d1 = np.log(np.divide(s,K)) + np.divide(np.multiply((0.5*np.square(sigma)+r),t),np.multiply(sigma,np.sqrt(t)))\n",
        "      return np.multiply(np.multiply(s,norm.pdf(d1)),np.sqrt(t))\n",
        "\n",
        "  def newton(self,f,df,x0,tol):\n",
        "    '''\n",
        "    Newtons method\n",
        "    '''\n",
        "      x = x0\n",
        "      maxit = 100\n",
        "      it = 0\n",
        "      ind = np.abs(f(x)/df(x))>tol\n",
        "      while it < maxit and np.any(ind):\n",
        "          # Iterate on the indices that haven't yet converged\n",
        "          ind = np.abs(f(x)/df(x))>tol\n",
        "          x[ind]=x[ind]-np.divide(f(x),df(x))[ind]\n",
        "          it=it+1\n",
        "          # new set of indices to iterate on\n",
        "      if np.any(ind):\n",
        "          print('Warning: newton did not converge')\n",
        "      else:\n",
        "          print('converged in {it} iterations'.format(it = it))\n",
        "      return x\n",
        "\n",
        "  def price_AH_BS(self,data):\n",
        "    '''\n",
        "    Function that passes data to the correct functions to price\n",
        "    '''\n",
        "    X_reg = self.create_regression_data(data)\n",
        "    vol_reg = self.linreg.predict(X_reg)\n",
        "    y_reg = self.calculate_prices(vol_reg,data)\n",
        "    return y_reg"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "B1LS85qygmfp",
        "outputId": "ab4515e5-8996-486b-e42b-7d7ff45e6e22"
      },
      "source": [
        "train = option_data[(option_data['date'] >= pd.Timestamp(2003,1,1)) & (option_data['date'] < pd.Timestamp(2006,7,1))]\n",
        "test = option_data[(option_data['date'] >= pd.Timestamp(2006,7,1)) & (option_data['date'] < pd.Timestamp(2007,1,1))]\n",
        "market_model=AdHocBlackScholes(train)\n",
        "print(market_model.price_AH_BS(test)[0:10])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "converged in 7 iterations\n",
            "[0.         0.         0.         0.         0.         0.45343296\n",
            " 2.23264765 4.03344775 5.85395994 7.69184908]\n",
            "5.4712283265930195e-06\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:12: SettingWithCopyWarning: \n",
            "A value is trying to be set on a copy of a slice from a DataFrame.\n",
            "Try using .loc[row_indexer,col_indexer] = value instead\n",
            "\n",
            "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
            "  if sys.path[0] == '':\n",
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:12: SettingWithCopyWarning: \n",
            "A value is trying to be set on a copy of a slice from a DataFrame.\n",
            "Try using .loc[row_indexer,col_indexer] = value instead\n",
            "\n",
            "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
            "  if sys.path[0] == '':\n"
          ],
          "name": "stderr"
        }
      ]
    }
  ]
}