A Nonparametric Approach to Pricing and Hedging Derivative Securities Via Learning Networks





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    • Hutchinson is from PHZ Partners, Cambridge, Massachusetts. Lo is from the Sloan School of Management, Massachusetts Institute of Technology. Poggio is from the Artificial Intelligence Laboratory and the Center for Biological and Computational Learning, Massachusetts Institute of Technology. This article reports research done within the Massachusetts Institute of Technology Artificial Intelligence Laboratory and the Sloan School of Management's Research Program in Computational Finance. We thank Harrison Hong and Terence Lim for excellent research assistance, and Petr Adamek, Federico Girosi, Chung-Ming Kuan, Barbara Jansen, Blake LeBaron, and seminar participants at the DAIS Conference, the Harvard Business School, and the American Finance Association for helpful comments and discussion. Hutchinson and Poggio gratefully acknowledge the support of an ARPA AASERT grant administered under the Office of Naval Research contract N00014-92-J-1879. Additional support was provided by the Office of Naval Research under contract N00014-93-1-0385, by a grant from the National Science Foundation under contract ASC-9217041 (this award includes funds from ARPA provided under the HPCC program), by the Research Program in Computational Finance, and by Siemens AG. A portion of this research was conducted during Lo's tenure as an Alfred P. Sloan Research Fellow.


We propose a nonparametric method for estimating the pricing formula of a derivative asset using learning networks. Although not a substitute for the more traditional arbitrage-based pricing formulas, network-pricing formulas may be more accurate and computationally more efficient alternatives when the underlying asset's price dynamics are unknown, or when the pricing equation associated with the no-arbitrage condition cannot be solved analytically. To assess the potential value of network pricing formulas, we simulate Black-Scholes option prices and show 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 networks, multilayer perceptron networks, and projection pursuit. To illustrate the practical relevance of our network pricing approach, we apply it to the pricing and delta-hedging of S&P 500 futures options from 1987 to 1991.