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Option Pricing Under Skewness and Kurtosis Using a Cornish–Fisher Expansion

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  • Sofiane Aboura
  • Didier Maillard

Abstract

This paper revisits the pricing of options, in a context of financial stress, when the underlying asset's returns displays skewness and excess kurtosis. For that purpose, we use a Cornish–Fisher transformation for valuing option contracts with an exact formula allowing for heavy‐tails. An application to the S&P 500 stock index option contracts is carried out during both stress (October 2008) and calm (May 2015) periods. It provides evidence about the capability of the Cornish–Fisher model to fairly price options during a period of stress without violating the skewness–kurtosis boundaries given its large domain of validity. © 2016 Wiley Periodicals, Inc. Jrl Fut Mark 36:1194–1209, 2016

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  • Sofiane Aboura & Didier Maillard, 2016. "Option Pricing Under Skewness and Kurtosis Using a Cornish–Fisher Expansion," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 36(12), pages 1194-1209, December.
    • Handle: RePEc:wly:jfutmk:v:36:y:2016:i:12:p:1194-1209
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    2. Brenda Castillo-Brais & Ángel León & Juan Mora, 2022. "Estimating Value-at-Risk and Expected Shortfall: Do Polynomial Expansions Outperform Parametric Densities?," Mathematics, MDPI, vol. 10(22), pages 1-17, November.
    3. Charles-Olivier Amédée-Manesme & Fabrice Barthélémy & Didier Maillard, 2019. "Computation of the corrected Cornish–Fisher expansion using the response surface methodology: application to VaR and CVaR," Annals of Operations Research, Springer, vol. 281(1), pages 423-453, October.
    4. Ulze, Markus & Stadler, Johannes & Rathgeber, Andreas W., 2021. "No country for old distributions? On the comparison of implied option parameters between the Brownian motion and variance gamma process," The Quarterly Review of Economics and Finance, Elsevier, vol. 82(C), pages 163-184.

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