Skewness and kurtosis in s&p 500 index returns implied by option prices

Charles J. Corrado, Tie Su

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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.

Original languageEnglish (US)
Pages (from-to)175-192
Number of pages18
JournalJournal of Financial Research
Volume19
Issue number2
DOIs
StatePublished - Jun 1996

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ASJC Scopus subject areas

  • Accounting
  • Finance

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