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.

One of the major premises of efficient market theory is that the market quickly impounds any publicly available information, including macroeconomic information, that might be used to predict stock prices. It is only new-and especially new and unpredictable-information that moves prices, and yet many studies examine only announcements that have a predictable component. Researchers typically select a proxy for the anticipated portion of the news announcement and then test the market's reaction to the unanticipated portion of the announcement. However, the process of separating the anticipated and unanticipated portions of news announcements is critical to conclusions that can be drawn about price changes, the speed of adjustment, and trading activities. We avoid this separation problem by looking at fully unanticipated events. * We would like to thank Laura Starks and an anonymous referee for helpful suggestions, Ron Howren for computer support, Eric Schuster and Bob Hebert for gathering the sample, and Sandra Sizer Moore for editorial assistance. Ajay Patel thanks the Research Fellowship Program at Wake Forest University's Babcock Graduate School of Management for partial support of this project. Tie Su acknowledges financial support from the Research Council, University of Miami. The usual disclaimer applies.

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The Black-Scholes* option pricing model is commonly applied to value a wide range of option contracts. However, the model often inconsistently prices deep in-the-money and deep out-of-the-money options. Options professionals refer to this well-known phenomenon as a volatility 'skew' or 'smile'. In this paper, we examine an extension of the Black-Scholes model developed by Corrado and Su that suggests skewness and kurtosis in the option-implied distributions of stock returns as the source of volatility skews. Adapting their methodology, we estimate option-implied coefficients of skewness and kurtosis for four actively traded stock options. We find significantly nonnormal skewness and kurtosis in the option-implied distributions of stock returns.Stock Options Implied Volatility Skewness Kurtosis,

If option implied volatility is an unbiased, efficient forecast of future return volatility in the underlying asset, then we should be able to predict its path around macroeconomic announcements from responses in cash markets. Regressions show that volatilities rise the afternoon before announcements that move cash markets, and that post-announcement volatilities return to normal as rapidly as cash prices do. Although implied volatilities are predictable, the Treasury options market is efficient since informed traders do not earn arbitrage profits once we account for trading costs.