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Implied Volatility Skews and Stock Index Skewness and Kurtosis Implied by S&P 500 Index Option Prices

The Black-Scholes (1973) option pricing model is used to value a wide range of option contracts. However, the model often inconsistently prices deep in-themoney and deep out-of-the-money options. Options’ professionals refer to this phenomenon as a volatility ‘skew’ or ‘smile.’ In this paper, we apply an extension of the Black-Scholes model developed by Jarrow and Rudd (1982) to an investigation of S&P 500 index option prices. We find that non-normal skewness and kurtosis in option-implied distributions of index returns contribute significantly to the phenomenon of volatility skews.