A NONPARAMETRIC APPROACH TO PRICING AND HEDGING DERIVATIVE SECURITIESVIA LEARNING NETWORKS

We propose a nonparametric method for estimating the pricing formula o f a derivative asset using learning networks. Although not a substitut e for the more traditional arbitrage-based pricing formulas, network-p ricing formulas may be more accurate and computationally more efficien t alternatives when the underlying asset's price dynamics are unknown, or when the pricing equation associated with the no-arbitrage conditi on cannot be solved analytically. To assess the potential value of net work pricing formulas, we simulate Black-Scholes option prices and sho w that learning networks can recover the Black-Scholes formula from a two-year training set of daily options prices, and that the resulting network formula can be used successfully to both price and delta-hedge options out-of-sample. For comparison, we estimate models using four popular methods: ordinary least squares, radial basis function network s, multilayer perceptron networks, and projection pursuit. To illustra te the practical relevance of our network pricing approach, we apply i t to the pricing and delta-hedging of S&P 500 futures options from 198 7 to 1991.