A neural network versus Black-Scholes: A comparison of pricing and hedging performances

Henrik Amilon

Research output: Contribution to journalArticlepeer-review

40 Citations (SciVal)


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 to 1999. The relevance of a hedge-analysis is stressed further in this paper. As benchmarks, the Black-Scholes model with historical and implied volatility estimates are used. Comparisons reveal that the neural network models outperform the benchmarks both in pricing and hedging performances. A moving block bootstrap is used to test the statistical significance of the results. Although the neural networks are superior, the results are sometimes insignificant at the 5% level. Copyright (C) 2003 John Wiley Sons, Ltd.
Original languageEnglish
Pages (from-to)317-335
JournalJournal of Forecasting
Issue number4
Publication statusPublished - 2003

Subject classification (UKÄ)

  • Economics


  • neural networks
  • option pricing
  • hedging
  • bootstrap
  • inference
  • statistical


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