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Pricing and hedging S&P 500 index options with Hermite polynomial approximation: empirical tests of Madan and Milne's model
Author(s) -
Ané Thierry
Publication year - 1999
Publication title -
journal of futures markets
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.88
H-Index - 55
eISSN - 1096-9934
pISSN - 0270-7314
DOI - 10.1002/(sici)1096-9934(199910)19:7<735::aid-fut1>3.0.co;2-w
Subject(s) - kurtosis , black–scholes model , skewness , valuation of options , hermite polynomials , index (typography) , econometrics , economics , mathematics , range (aeronautics) , finite difference methods for option pricing , mathematical economics , statistics , computer science , mathematical analysis , volatility (finance) , materials science , world wide web , composite material
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