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Option-pricing formulas with skewness and kurtosis

Author

Listed:
  • Pakorn Aschakulporn

    (University of Otago, Department of Accountancy and Finance, Otago Business School)

  • Jin E. Zhang

    (University of Otago, Department of Accountancy and Finance, Otago Business School)

Abstract

This paper provides a comprehensive review of option-pricing formulas with skewness and kurtosis. The formulas were obtained using the risk-neutral valuation method with return distribution modelled by the Gram-Charlier density. This paper presents a correct and exact formula, points out the errors in the existing literature, and discusses the relationship between different formulas. This formula can easily be used by practitioners and academics to introduce skewness and kurtosis to the standard Black–Scholes formula and/or test more advanced models.

Suggested Citation

  • Pakorn Aschakulporn & Jin E. Zhang, 2026. "Option-pricing formulas with skewness and kurtosis," Review of Derivatives Research, Springer, vol. 29(1), pages 1-23, December.
    • Handle: RePEc:kap:revdev:v:29:y:2026:i:1:d:10.1007_s11147-025-09224-5
    DOI: 10.1007/s11147-025-09224-5
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    Keywords

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    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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