A neural network-based method for pricing American options and assessing implied volatility under uncertainty

Abstract

American option pricing serves as a foundational concept in modern finance and investors commonly embrace this financial derivative for its advantageous flexibility in terms of exercise timing. Within the uncertainty theory literature, the calibration of the American option pricing model has not been explored to facilitate a meaningful comparison between the model-driven option prices and those observed in the market. This study aims to fill this gap by considering the asset price dynamic as some common uncertain models, such as the geometric Liu (GL) process, uncertain mean-reverting (UMR) process, and uncertain exponential mean-reverting (UEMR) process. This paper presents a novel hybrid method to calibrate the American option pricing model based on the uncertain option pricing model and artificial neural network (ANN). The proposed hybrid structure retains the unknown parameters involved in uncertain model while incorporating neural network techniques to improve accuracy in real market applications. Given that the realization of volatility smiles can help investors identify mispriced options and make more informed investment decisions, this study undertakes the first evaluation of the volatility smile for American options in the uncertain environment using an ANN. Empirical studies on the SPY market show that uncertain models equipped with the ANN, when compared to the common option pricing models, provide more accurate evaluations of American option prices and their volatility smile.