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Skewness and Kurtosis in S&P 500 Index Returns Implied by Option Prices

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  • Corrado, Charles J
  • Su, Tie

Abstract

The Black-Scholes (1973) model frequently misprices deep-in-the-money and deep-out-of-the-money options. Practitioners popularly refer to these strike price biases as volatility smiles. In this paper we examine a method to extend the Black-Scholes model to account for biases induced by nonnormal skewness and kurtosis in stock return distributions. The method adapts a Gram-Charlier series expansion of the normal density function to provide skewness and kurtosis adjustment terms for the Black-Scholes formula. Using this method, we estimate option-implied coefficients of skewness and kurtosis in S&P 500 stock index returns. We find significant nonnormal skewness and kurtosis implied by option prices.

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Bibliographic Info

Article provided by Southern Finance Association & Southwestern Finance Association in its journal Journal of Financial Research.

Volume (Year): 19 (1996)
Issue (Month): 2 (Summer)
Pages: 175-92

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Handle: RePEc:bla:jfnres:v:19:y:1996:i:2:p:175-92

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Web page: http://www.southwesternfinance.org/
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