cos_method_results.py

from cos_method import *

class CosResults(CosMethod):

    def price_option_Cos():

        S0_list = [100, 110, 120]

        for S0 in S0_list:
             
            cos_object = CosMethod(
                        r=0.04,
                        sigma=0.30,
                        S0=S0,
                        K=110,
                        T=1,
                        L=11,
                        n_iterations=64)

            cos_object.characteristic_function()
            cos_object.compute_Fn()
            cos_object.compute_Gn()
            price_est = cos_object.compute_price_approximation()
            price_analytical = cos_object.analytical_solution()

            print(f"(COS-estimate,BS) = {price_est,price_analytical} for params (r = {cos_object.r}, vol = {cos_object.sigma}, S0 = {cos_object.S0},K = {cos_object.K},T = {cos_object.T})")

    def convergence_to_bs():

        S0_list = [100, 110, 120]

        price_ests_list = []  # A list of lists
        price_analytical_list = []
        n_terms = np.arange(1, 65, 1)

        # Prepare subplots arranged horizontally
        fig, axes = plt.subplots(nrows=2, ncols=3, figsize=(12, 7), dpi=300)
        fig.tight_layout(pad=4.0)

        for idx, S0 in enumerate(S0_list):
            price_ests = []

            for n in n_terms:
                cos_object = CosMethod(
                    r=0.04,
                    sigma=0.30,
                    S0=S0,
                    K=110,
                    T=1,
                    L=11,
                    n_iterations=n,
                )
                
                cos_object.characteristic_function()
                cos_object.compute_Fn()
                cos_object.compute_Gn()
                price_est = cos_object.compute_price_approximation()
                price_ests.append(price_est)
            price_ests_list.append(price_ests)

            price_analytical = cos_object.analytical_solution()  # Obtain BS solution
            price_analytical_list.append(price_analytical)

            # Plotting on separate subplots arranged horizontally
            axes[0, idx].plot(n_terms, price_ests, color="blue", label=f"COS-Method S0 = {S0}")
            axes[0, idx].axhline(price_analytical, linestyle="--", color="green", label=f"BS Solution S0 = {S0}")
            axes[0,idx].set_xlabel("Number of terms")
            axes[0,idx].set_ylabel("Price")
            axes[0, idx].legend(fontsize = 10)


            # Calculating and plotting the error on the corresponding subplot below
            error = np.abs(np.array(price_ests) - price_analytical)
            axes[1, idx].plot(n_terms, error, color="red", label=f"Error for S0 = {S0}")
            axes[1, idx].set_xlabel("Number of terms")
            axes[1,idx].set_ylabel("Error")
            axes[1, idx].legend(fontsize = 10)


        plt.savefig("Cos-Convergence", dpi = 300)
        plt.show()
        

        
if __name__ == "__main__":

    CosResults.convergence_to_bs()