A Neural Network Versus Black-Scholes: A Comparison of Pricing and Hedging Performances

The Black-Scholes formula is a well-known model for pricing and hedging derivative securities. It relies, however, on several highly questionable assumptions. This paper examines whether a neural network (MLP) can be used to find a call option pricing formula better corresponding to market prices and the properties of the underlying asset than the Black-Scholes formula. The neural network method is applied to the out-of-sample pricing and delta-hedging of daily Swedish stock index call options from 1997-1999. The relevance of a hedge-analysis is stressed further in this paper. As benchmarks, the Black-Scholes model with historical and implicit volatility estimates is used. Comparisons reveal that the neural network models outperform the benchmarks both in pricing and hedging performances. A moving block bootstrap procedure is used to test the statistical significance of the results. Although the neural networks are superiour, the results are sometimes insignificant at the 5% level.