Variance Risk Premia

44 Pages Posted: 17 Aug 2004 Last revised: 25 Oct 2007

See all articles by Liuren Wu

Liuren Wu

City University of New York, CUNY Baruch College - Zicklin School of Business

Peter Carr

New York University Finance and Risk Engineering

Date Written: October 24, 2007

Abstract

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

Keywords: Stochastic volatility, variance risk premia, variance swap, volatility swap, option pricing, expectation hypothesis

JEL Classification: G10, G12, G13, C51

Suggested Citation

Wu, Liuren and Carr, Peter P., Variance Risk Premia (October 24, 2007). AFA 2005 Philadelphia Meetings. Available at SSRN: https://ssrn.com/abstract=577222 or http://dx.doi.org/10.2139/ssrn.577222

Liuren Wu (Contact Author)

City University of New York, CUNY Baruch College - Zicklin School of Business ( email )

One Bernard Baruch Way
Box B10-247
New York, NY 10010
United States
646-312-3509 (Phone)
646-312-3451 (Fax)

HOME PAGE: http://faculty.baruch.cuny.edu/lwu/

Peter P. Carr

New York University Finance and Risk Engineering ( email )

6 MetroTech Center
Brooklyn, NY 11201
United States
9176217733 (Phone)

HOME PAGE: http://engineering.nyu.edu/people/peter-paul-carr

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