SKEWNESS AND KURTOSIS IN S&P 500 INDEX RETURNS IMPLIED BY OPTION PRICES

Authors


  • Research for this paper was supported by a grant from the University of Missouri System Research Board. An earlier version of this paper entitled “Implied Stochastic Factors in Option Prices” received the American Association of Individual Investors (AAII) award for the best paper in Investments presented at the 1994 Southern Finance Association Meetings. We are grateful for helpful comments by William T. Moore and an anonymous referee.

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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