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

  • Published: Apr 30, 2012
  • Pages: 851-889
  • DOI: 10.1111/j.1540-6261.1994.tb00081.x


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.

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