Integration of Fractional Order Black-Scholes Merton with Neural Network

This study presents a novel approach to enhance option pricing accuracy by introducing the Fractional Order Black-Scholes-Merton (FOBSM) model. FOBSM combines elements of the traditional Black-Scholes-Merton (BSM) model with the flexibility of neural networks (NN). American options pose unique pricing challenges due to free boundary difficulties. On the other hand, traditional models like BSM struggle to accurately represent market pricing. The challenge is to develop a pricing model that better captures the tail behavior, memory effects, volatility clustering, long-term dependencies, and skewness inherent in financial data, while simultaneously utilizing the theoretical underpinnings of BSM and fractional calculus. The research gap arises from the absence of a comprehensive framework that integrates fractional calculus and neural networks to enhance option pricing accuracy in complex diffusion dynamics scenarios. Since FOBSM captures memory characteristics in sequential data, it is better at simulating real-world systems than integer-order models. The findings reveal that in complex diffusion dynamics, this hybridization approach in option pricing improves the accuracy of price predictions.