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Journal of Financial Econometrics Advance Access originally published online on September 7, 2006
Journal of Financial Econometrics 2006 4(4):636-670; doi:10.1093/jjfinec/nbl003
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© The Author 2006. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

Long Memory and the Relation Between Implied and Realized Volatility

Federico M. Bandi
     University of Chicago

Benoit Perron
     Université de Montréal, CIREQ, CIRANO

Address correspondence to Benoit Perron, Département de sciences économiques, Université de Montréal, C.P. 6128, Succursale centre-ville, Montréal, Québec, H3C 3J7, Canada or e-mail: benoit.perron{at}umontreal.ca.

We argue that the predictive regression between implied volatility (regressor) and realized volatility over the remaining life of a European option (regressand) is likely to be a fractional cointegrating relation. Because cointegration is associated with long-run comovements, this classical regression cannot be used to test for option market efficiency and short-term unbiasedness of implied volatility as a predictor of realized volatility. Using narrow-band spectral methods, we provide consistent estimates of the long-run relation between implied and realized volatility even when implied volatility is measured with error and/or volatility is priced but the volatility risk premium is unobservable. Although little can be said about short-term unbiasedness, our results largely support a notion of long-run unbiasedness of implied volatility as a predictor of realized volatility.

KEYWORDS: fractional cointegration, implied volatility, long memory, predictive regression, realized volatility

Received July 19, 2006; revised August 4, 2006; accepted August 8, 2006


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