Alternative Neural Network Approach for Option Pricing and Hedging

Abstract

Since its introduction in 1973, the Black-Scholes model has found increasingly more resistance in application. In order to use Black-Scholes to price any option, one needs to know the implied volatility surface. The existence of such surface is an evidence of misspecification of the model. In this case, the problem is with the assumption of a geometric Brownian motion for the stock price process. There is strong empirical evidence that stocks do not follow such process. However, no agreement has been reached on what is the best distribution to use. Neural Network approaches the problem very differently. Essentially, a Neural Network is a non-parametric estimation technique. It does not make any distributional assumption regarding the underlying variable. Instead, it puts up a formula with a set of unknown parameters and let the optimization routine search for the parameters best fitted to the desired results. Hutchinson-Lo-Poggio (1994) showed that it is indeed possible to use a Neural Network to price S&P futures options. In this paper, we will continue with this line of research. Specifically, we will examine the best way to set up and train a Neural Network for option pricing and hedging. We will also investigate if a Neural Network could produce better hedging parameters than the standard option pricing model. We use S&P futures options data covering the period 1990–2000.