The Relation Between Physical and Risk-Neutral Cumulants

44 Pages Posted: 10 Mar 2010 Last revised: 16 Mar 2010

See all articles by Eric C. Chang

Eric C. Chang

University of Hong Kong - School of Business

Jin E. Zhang

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

Huimin Zhao

The University of Hong Kong

Multiple version iconThere are 2 versions of this paper

Date Written: February 2010

Abstract

Variance swaps are natural instruments for investors taking directional bets on volatility and are often used for portfolio protection. But the crucial observation suggests that derivative professionals may desire to hedge beyond volatility risk and there exists the need to hedge higher-moment market risks, such as skewness and kurtosis risks. We propose new derivative contracts: skewness swap and kurtosis swap, which trade the forward realized third and fourth cumulants. Using S&P 500 index options data from 1996 to 2005, we document the returns of these swap contracts, i.e., skewness risk premium and kurtosis risk premium. We find that the skewness risk premium is significantly negative and kurtosis risk premium for 90 day maturity is significantly positive.

Keywords: Skewness swap, Kurtosis swap, Equity risk premium, Variance risk premium, Skewness risk premium, Kurtosis risk premium

JEL Classification: G12, G13

Suggested Citation

Chang, Eric Chieh C. and Zhang, Jin E. and Zhao, Huimin, The Relation Between Physical and Risk-Neutral Cumulants (February 2010). Available at SSRN: https://ssrn.com/abstract=1566717 or http://dx.doi.org/10.2139/ssrn.1566717

Eric Chieh C. Chang

University of Hong Kong - School of Business ( email )

Meng Wah Complex
Pokfulam Road
Hong Kong
China

Jin E. Zhang

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

Dunedin, 9054
New Zealand
64 3 479 8575 (Phone)
64 3 479 8171 (Fax)

HOME PAGE: http://sites.google.com/site/jinzhanghomepage/home

Huimin Zhao (Contact Author)

The University of Hong Kong ( email )

School of Business, HKU,
Pokfulam Road
Hong Kong, Hong Kong HK
China
22415685 (Phone)

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