Option-pricing formulas with skewness and kurtosis

Pakorn Aschakulporn; Jin E. Zhang

doi:10.1007/s11147-025-09224-5

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Option-pricing formulas with skewness and kurtosis

Journal article

Open access

Peer reviewed

Option-pricing formulas with skewness and kurtosis

Pakorn Aschakulporn and Jin E. Zhang

Review of derivatives research, Vol.29(1), 2

19/11/2025

DOI: https://doi.org/10.1007/s11147-025-09224-5

Handle:

https://hdl.handle.net/10523/48894

Abstract

Gram-Charlier densities

Option-pricing

skewness

Kurtosis

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.

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Record Identifier: 9926793258201891
Title: Option-pricing formulas with skewness and kurtosis
Creators: Pakorn Aschakulporn
Jin E. Zhang
Publication Details: Review of derivatives research, Vol.29(1), 2
Academic Unit: Accountancy and Finance
Publisher: Springer Nature
Grant note: University of Otago Doctoral Scholarship; University of Otago
Date published ; e-published: 19/11/2025
Copyright: Copyright © The Author(s) 2025. All rights reserved. This work was first published in X (Springer Nature). The open access link to the subscription article is provided under the Springer Nature SharedIt Content-Sharing Initiative (https://www.springernature.com/gp/researchers/sharedit) making the view-only full-text article freely and legally accessible to anyone for research purposes and private study via the link: https://rdcu.be/eRYBV.
Comment: The published version is not available in full-text in OUR Archive. Where available, a link to the published version is provided (check the DOI and/or the Files and links section). The full-text item may be open access on the publisher's website. An earlier version of the work (such as authors' accepted manuscript following peer-review or unreviewed preprint/author's original version) may be available in the Files and links section of this record. Alternatively, readers may have subscription access to the full-text from the publisher.
Language: English
Resource Type ; Subtype: Journal article