American Options: A Fractional-Order Black-Scholes Merton Approach with Neural Network

The Black-Scholes-Merton model (BSM) is frequently used to evaluate the fair price of a call or put option based on volatility (σ), option type (C), underlying price (S <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</inf> ), period (t), strike price (K), and risk-free rate (r). However, the model faces challenges in capturing dynamic market conditions. To overcome this problem, this study introduces an integrated approach that integrates Fractional Order BSM (FOBSM) with a feed-forward Neural Network for American put option pricing. This approach helps capture the intricacies of dynamic markets and enhances the model adaptability to unpredictable market behaviors. The proposed model is evaluated using real-life Bitcoin (cryptocurrency) option data emphasizing short-term maturities. The error comparison reveals that the performance of FOBSM with NN is superior to that of existing popular BSM variants, such as, conventional BSM, Binomial tree, and BSM with LSM (Longstaff-Schwartz Least-Squares Monte Carlo).