A Black-Scholes-integrated Gaussian Process Model for American Option Pricing

Abstract

Acknowledging the lack of option pricing models that simultaneously have high prediction power, high computational efficiency, and interpretations that abide by financial principles, we suggest a Black-Scholes-integrated Gaussian process (BSGP) learning model that is capable of making accurate predictions backed with fundamental financial principles. Most data-driven models boast strong computational power at the expense of inferential results that can be explained with financial principles. Vice versa, most closed-form stochastic models (principle-driven) exhibit inferential results at the cost of computational efficiency. By integrating the Black-Scholes computed price for an equivalent European option into the mean function of the Gaussian process, we can design a learning model that emphasizes the strengths of both data- driven and principle-driven approaches. Using American (SPY) call and put option price data from 2019 May to June, we condition the Black-Scholes mean Gaussian Process prior with observed data to derive the posterior distribution that is used to predict American option prices. Not only does the proposed BSGP model provide accurate predictions, high computational efficiency, and interpretable results, but it also captures the discrepancy between a theoretical option price approximation derived by the Black-Scholes and predicted price from the BSGP model.