Available at: https://digitalcommons.calpoly.edu/theses/3148
Date of Award
9-2025
Degree Name
MS in Statistics
Department/Program
Statistics
College
College of Science and Mathematics
Advisor
Trevor D. Ruiz
Advisor Department
Statistics
Advisor College
College of Science and Mathematics
Abstract
Accurately pricing American options with market data presents a significant challenge, as foundational models like the Black-Scholes-Merton (BSM) model rely on assumptions that deviate from real-world financial data -- such as log-normal returns, constant volatility, and no dividends -- and fail to account for the key early exercise feature of American options. While parametric models can adjust for these features, the complexity of the resulting models renders them prohibitively difficult to apply in practice for nonspecialists. In response, modern machine learning (ML) techniques provide a set of flexible and powerful alternatives, and recent research has explored the application of ML for various purposes in quantitative finance. This study investigates American option pricing methodologies using end-of-day SPY ETF data from February 2012 to May 2024, focusing on a multilayer perceptron (MLP) neural network architecture that utilizes a small number of core inputs: the underlying SPY price, strike price, time to expiry, risk-free interest rate, historical volatility, implied volatility, dividend yield, and an indicator for ex-dividend date. Through a walk-forward cross-validation approach, this research aims to determine whether MLPs can outperform BSM for pricing options, as measured by out-of-sample RMSE, using end-of-day data with midpoint option prices as the target and either realized volatility or implied volatility as inputs. It also examines the extent to which unconstrained neural networks violate fundamental no-arbitrage conditions when pricing American options. The results indicate that MLPs are more flexible in capturing option price behavior, especially when using implied volatility inputs. However, unconstrained networks tend to violate key no-arbitrage principles. This limitation underscores the importance of incorporating structural constraints to enhance robustness and relevance, but also opens the door to developing models that can support trading strategies and create an edge in the market.