Statistical Papers

, 32:299

Skewness, kurtosis, and black-scholes option mispricing

  • R. Geske
  • W. Torous
Articles

DOI: 10.1007/BF02925505

Cite this article as:
Geske, R. & Torous, W. Statistical Papers (1991) 32: 299. doi:10.1007/BF02925505

Abstract

The Black-Scholes 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 Black-Scholes 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 Black-Scholes model's pricing performance with respect to estimated volatility.

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • R. Geske
    • 1
  • W. Torous
    • 1
  1. 1.Anderson Graduate School of ManagementUCLALos AngelesU.S.A.