Skewness, kurtosis, and blackscholes option mispricing
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The BlackScholes option pricing model assumes that (instantaneous) common stock returns are normally distributed. However, the observed distribution exhibits deviations from normality; in particular skewness and kurtosis. We attribute these deviations to gross data errors. Using options' transactions data, we establish that the sample standard deviation, sample skewness, and sample kurtosis contribute to the BlackScholes model's observed mispricing of a sample from the Berkeley Options Data Base of 2323 call options written on 88 common stocks paying no dividends during the options'life. Following Huber's statement that the primary case for robust statistics is when the shape of the observed distribution deviates slightly from the assumed distribution (usually the Gaussian), we show that robust volatility estimators eliminate the mispricing with respect to sample skewness and sample kurtosis, and significantly improve the BlackScholes model's pricing performance with respect to estimated volatility.
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 Title
 Skewness, kurtosis, and blackscholes option mispricing
 Journal

Statistical Papers
Volume 32, Issue 1 , pp 299309
 Cover Date
 19911201
 DOI
 10.1007/BF02925505
 Print ISSN
 09325026
 Online ISSN
 16139798
 Publisher
 SpringerVerlag
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