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Pricing and hedging S&P 500 index options with Hermite polynomial approximation: empirical tests of Madan and Milne's model

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  • Thierry Ané

Abstract

The universal use of the Black and Scholes option pricing model to value a wide range of option contracts partly accounts for the almost systematic use of Gaussian distributions in finance. Empirical studies, however, suggest that there is an information content beyond the second moment of the distribution that must be taken into consideration.This article applies a Hermite polynomial‐based model developed by Madan and Milne (1994) to an investigation of S&P 500 index option prices from the CBOE when the distribution of the underlying index is unknown. The model enables us to incorporate the non‐normal skewness and kurtosis effects empirically observed in option‐implied distributions of index returns. Out‐of‐sample tests confirm that the model outperforms Black and Scholes in terms of pricing and hedging. © 1999 John Wiley & Sons, Inc. Jrl Fut Mark 19: 735–758, 1999

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  • Thierry Ané, 1999. "Pricing and hedging S&P 500 index options with Hermite polynomial approximation: empirical tests of Madan and Milne's model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 19(7), pages 735-758, October.
    • Handle: RePEc:wly:jfutmk:v:19:y:1999:i:7:p:735-758
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    Cited by:

    1. V. L. Martin & G. M. Martin & G. C. Lim, 2005. "Parametric pricing of higher order moments in S&P500 options," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(3), pages 377-404.
    2. Sofiane Aboura & Didier Maillard, 2016. "Option Pricing Under Skewness and Kurtosis Using a Cornish–Fisher Expansion," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 36(12), pages 1194-1209, December.
    3. Fleming, Euan & Villano, Renato & Williamson, Brendon, 2013. "Structuring Exotic Options Contracts on Water to Improve the Efficiency of Resource Allocation in the Australian Water Market," Papers 234295, University of Melbourne, Melbourne School of Land and Environment.

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