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

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Listed:
  • James M. Hutchinson
  • Andrew W. Lo
  • Tomaso Poggio

Abstract

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 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.

Suggested Citation

  • James M. Hutchinson & Andrew W. Lo & Tomaso Poggio, 1994. "A Nonparametric Approach to Pricing and Hedging Derivative Securities Via Learning Networks," NBER Working Papers 4718, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:4718 Note: AP
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    1. Stiglitz, Joseph E., 1983. "Some aspects of the taxation of capital gains," Journal of Public Economics, Elsevier, vol. 21(2), pages 257-294, July.
    2. Joel M. Dickson & John B. Shoven, 1993. "Ranking Mutual Funds on an After-Tax Basis," NBER Working Papers 4393, National Bureau of Economic Research, Inc.
    3. Constantinides, George M., 1984. "Optimal stock trading with personal taxes : Implications for prices and the abnormal January returns," Journal of Financial Economics, Elsevier, vol. 13(1), pages 65-89, March.
    4. Constantinides, George M, 1983. "Capital Market Equilibrium with Personal Tax," Econometrica, Econometric Society, vol. 51(3), pages 611-636, May.
    5. Lee, Charles M C & Shleifer, Andrei & Thaler, Richard H, 1990. "Closed-End Mutual Funds," Journal of Economic Perspectives, American Economic Association, vol. 4(4), pages 153-164, Fall.
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    More about this item

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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