Option pricing mechanisms driven by backward stochastic differential equations

Abstract

Abstract This study investigates an option pricing method called g-pricing based on backward stochastic differential equations combined with deep learning. We adopted a data-driven approach to find a market-appropriate generator of the backward stochastic differential equation, which is achieved by leveraging the universal approximation capabilities of neural networks. Option pricing, which is the solution to the equation, is approximated using a recursive procedure. The empirical results for the S&P 500 index options show that the proposed deep learning g-pricing model has lower absolute errors than the classical Black–Scholes–Merton model for the same forward stochastic differential equations. The g-pricing mechanism has potential applications in option pricing.

Keywords

• Option pricing
• Backward stochastic differential equation
• Numerical method
• Deep learning