On the Solution of the Black-Scholes Equation Using Feed-Forward Neural Networks

Abstract

This paper deals with a comparative numerical analysis of the Black-Scholes equation for the value of a European call option. Artificial neural networks are used for the numerical solution to this problem. According to this method we approximate the unknown function of the option value using a trial function which depends on a neural network solution and satisfies the given boundary conditions of the Black-Scholes equation. We consider some optimization methods not examined in the standard literature such as particle swarm optimization and the gradient-type monotone iteration process to obtain the unknown parameters of the neural network. Numerical results show that this proposed version of neural network method obtains all data from the terminal value and boundary conditions with sufficient accuracy.