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RFS Advance Access originally published online on April 10, 2008
Review of Financial Studies 2009 22(3):1311-1341; doi:10.1093/rfs/hhn038
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© The Author 2008. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Variance Risk Premiums

Peter Carr
Bloomberg LP and Courant Institute, New York University

Liuren Wu
Zicklin School of Business, Baruch College

Address correspondence to Liuren Wu, Department of Economics and Finance, Zicklin School of Business, Baruch College, CUNY, One Bernard Baruch Way, Box B10-225, New York, NY 10010; telephone: (646) 312-3509, fax: (646) 312-3451, e-mail: Liuren_Wu{at}baruch.cuny.edu.

JEL Classification: G10, G12, G13


  Abstract

We propose a direct and robust method for quantifying the variance risk premium on financial assets. We show that the risk-neutral expected value of return variance, also known as the variance swap rate, is well approximated by the value of a particular portfolio of options. We propose to use the difference between the realized variance and this synthetic variance swap rate to quantify the variance risk premium. Using a large options data set, we synthesize variance swap rates and investigate the historical behavior of variance risk premiums on five stock indexes and 35 individual stocks.

We thank Yacine Aït-Sahalia (the editor), an anonymous referee, and Turan Bali, David Bates, Menachem Brenner, Mikhail Chernov, Robert Engle, Stephen Figlewski, Rajna Gibson, Alfredo Ibanez, George Jiang, Dilip Madan, Steven Posner, Anders Bjerre Trolle, Benjamin Wurzburger, Jin Zhang, Chu Zhang, and seminar participants at the 5th Conference on Financial Risks at Verona (Italy), the 2005 American Finance Association meetings, Baruch College, Hong Kong University of Science and Technology, New York University, and University of Zurich for comments. We also thank David Hait and OptionMetrics for providing the option data, Alex Mayus for clarifying trading practices, and Rui Yao for help on data processing. We assume full responsibility for any remaining errors. Liuren Wu gratefully acknowledges the support by a grant from The City University of New York PSC-CUNY Research Award Program.


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