Beyond Black–Scholes: A Neural Networks-Based Approach to Options Pricing

Abstract

The paper presents two alternative schemes for pricing European and American call options, both based on artificial neural networks. The first method uses binomial trees linked to an innovative stochastic volatility model. The volatility model is based on wavelets and artificial neural networks. Wavelets provide a convenient signal/noise decomposition of the volatility in the non-linear feature space. Neural networks are used to infer future volatility levels from the wavelets feature space in an iterative manner. The bootstrap method provides the 95% confidence intervals for the options prices. In the second approach neural networks are trained with genetic algorithms in order to reverse-engineer the Black–Scholes formulae. The standard Black–Scholes model provides a starting point for an evolutionary training process, which yields improved options prices. Market options prices as quoted on the Chicago Board Options Exchange are used for performance comparison between the Black–Scholes model and the proposed options pricing schemes. The proposed models produce as good as and often better options prices than the conventional Black–Scholes formulae.