Pricing of Financial Derivatives: Focus on American Put Options

The first part introduces key financial derivative concepts, such as forwards, futures, swaps, and options. It provides an overview of basic pricing methods, including parameters like stock price, strike price, volatility, and time to maturity. The section also explains foundational models such as Black-Scholes, put-call parity, and Geometric Brownian Motion (GBM), supported by Python simulations to demonstrate how stock prices evolve. The second part delves into more complex exotic options like Bermuda options, barrier options, and Asian options. These options differ from standard ones in terms of payoff structures and risks. The section also includes Python code for pricing exotic options and simulating stock price behaviors. In addition, it covers portfolio management, focusing on risk measurement, variance, correlation, and optimization strategies for building portfolios with multiple assets, including minimum variance portfolios. The third part explores the use of machine learning for pricing American put options, contrasting it with traditional approaches like Longstaff-Schwartz’s LSM method. The section outlines the neural network model used to estimate the continuation value, improving the accuracy of option pricing. The final chapter provides a detailed explanation of the implementation, from data preparation to training and testing the model, with Python code integrated throughout.