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Option-Based Estimation of the Price of Coskewness and Cokurtosis Risk

Published online by Cambridge University Press:  10 November 2020

Peter Christoffersen ,
Mathieu Fournier ,
Kris Jacobs  and
Mehdi Karoui
Peter Christoffersen
Affiliation:
(deceased)
Mathieu Fournier
Affiliation:
HEC Montréal [email protected]
Kris Jacobs*
Affiliation:
University of [email protected]
Mehdi Karoui
Affiliation:
Ontario Municipal Employees Retirement System (OMERS) [email protected]
*
[email protected] (corresponding author)
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Abstract

We show that the prices of risk for factors that are nonlinear in the market return can be obtained using index option prices. The price of coskewness risk corresponds to the market variance risk premium, and the price of cokurtosis risk corresponds to the market skewness risk premium. Option-based estimates of the prices of risk lead to reasonable values of the associated risk premia. An analysis of factor models with coskewness risk indicates that the new estimates of the price of risk improve the models’ performance compared with regression-based estimates.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 56 , Issue 1 , February 2021 , pp. 65 - 91
Copyright
© The Author(s), 2020. Published by Cambridge University Press on behalf of Michael G. Foster School of Business, University of Washington

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Footnotes

Peter Christoffersen, our dear friend and coauthor, tragically passed away prior to the publication of this article. We thank the Bank of Canada, the Global Risk Institute, and the Social Sciences and Humanities Research Council (SSHRC) for financial support. For helpful comments, we thank Tim Bollerslev, Robert Dittmar (the referee), Adlai Fisher, Bryan Kelly, Eric Renault, Michael Rockinger, Sang Byung Seo, Bas Werker, Xiaoyan Zhang, and seminar participants at the 2015 American Finance Association (AFA) Meeting and the 2014 Society for Financial Econometrics (SoFiE) meeting.

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