Quantitative Analysis and Financial Modeling

This repository includes various algorithms and techniques used in financial modeling, stochastic processes, predictive analytics, and Monte Carlo simulations.

Table of Contents

• Monte Carlo Simulations
• Predictive Analytics
• Stochastic Calculus
• Stochastic Volatility Models
• License

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Monte Carlo Simulations

Monte Carlo methods for pricing, variance reduction, and risk-neutral simulations. The following notebooks are included:

• AntitheticVariatesVarianceReduction.ipynb: Demonstrates variance reduction using antithetic variates.
• ControlVariatesVarianceReduction.ipynb: Explores variance reduction via control variates.
• MCRiskNeutralOptionPricing.ipynb: Simulates European option pricing under the risk-neutral measure.
• MCSimulationStockPortfolio.ipynb: Models stock portfolio returns using correlated random walks.
• StockVolatilityOrnsteinUhlenbeck.ipynb: Simulates stock volatility using the Ornstein-Uhlenbeck process.

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Predictive Analytics

Analyzes historical data and predicts future trends using statistical and machine learning techniques. The following files are included:

• Maximum.csv: Historical maximum temperature data for predictive analysis.
• Minimum.csv: Historical minimum temperature data for predictive analysis.
• ModifiedOUTemperatureModel.ipynb: Stochastic temperature model based on Ornstein-Uhlenbeck dynamics.
• StatisticalAnalysis.ipynb: Exploratory data analysis and hypothesis testing.
• Temperature.ipynb: Machine learning regression models for temperature prediction.

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Stochastic Calculus

Implements stochastic processes used in quantitative finance. The following notebooks are included:

• BrownianMotion.ipynb: Simulates standard and multidimensional Brownian motion.
• GeometricBrownianMotion.ipynb: Models stock prices using the Geometric Brownian Motion (GBM) model.

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Stochastic Volatility Models

Volatility models for option pricing and financial risk management. The following notebooks are included:

• BreedenLitzenbergerStockVolatility.ipynb: Breeden-Litzenberger framework for volatility extraction.
• HestonModel.ipynb: Simulates stock prices using the Heston stochastic volatility model.

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License

This repository is licensed under the Apache-2.0 License. See the LICENSE file for details.