Adaptively trained Physics-informed Radial Basis Function Neural Networks for Solving Multi-asset Option Pricing Problems

TL;DR

This paper introduces an adaptive physics-informed radial basis function neural network that efficiently solves complex multi-asset option pricing PDEs by dynamically refining its architecture during training.

Contribution

It presents a novel adaptive training approach for a physics-informed RBF neural network tailored to multi-asset option pricing, enhancing accuracy and efficiency.

Findings

Accurately prices multi-asset options including European, exchange, and basket options.

Demonstrates improved convergence and handling of non-smooth payoffs.

Validates effectiveness through multiple complex financial derivatives.

Abstract

The present study investigates the numerical solution of Black-Scholes partial differential equation (PDE) for option valuation with multiple underlying assets. We develop a physics-informed (PI) machine learning algorithm based on a radial basis function neural network (RBFNN) that concurrently optimizes the network architecture and predicts the target option price. The physics-informed radial basis function neural network (PIRBFNN) combines the strengths of the traditional radial basis function collocation method and the physics-informed neural network machine learning approach to effectively solve PDE problems in the financial context. By employing a PDE residual-based technique to adaptively refine the distribution of hidden neurons during the training process, the PIRBFNN facilitates accurate and efficient handling of multidimensional option pricing models featuring non-smooth payoff conditions. The validity of the proposed method is demonstrated through a set of experiments encompassing a single-asset European put option, a double-asset exchange option, and a four-asset basket call option.