Evolutionary Neural Networks for Option Pricing: Multi-Assets Option and Exotic Option

Abstract

This paper presents a novel framework based on the evolutionary neural network to solve the generalized Black-Scholes equation arising in the financial market efficiently and accurately. We first employ evolutionary neural networks to parameterize the Partial Differential Equations (PDEs) involved in option pricing. This approach allows us to simplify the Black-Scholes PDEs and convert them into the corresponding Ordinary Differential Equations (ODEs). Thus we can use standard ODE solvers such as Euler’s method to solve the simplified ODE problem. The proposed framework is flexible and can handle various boundary conditions and terminal conditions, allowing customization based on specific market requirements and scenarios. Moreover, our method offers a reliable and deterministic solution methodology for the pricing framework, as it does not rely on stochastic training. Unlike other approaches that incorporate stochastic elements in their training process, our method eliminates the need for such training and provides consistent results. This deterministic nature enhances the reliability and stability of our approach, making it well-suited for real-world applica- tions in option pricing and financial markets. The experiments on multiple settings are carried out to illustrate the applicability and accuracy of the proposed framework.