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Journal of Financial Econometrics Advance Access published online on September 7, 2006
Journal of Financial Econometrics, 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
Received July 19, 2006
Revised August 4, 2006
Accepted August 8, 2006

Article

Long Memory and the Relation Between Implied and Realized Volatility

Federico M. Bandi 1 and Benoit Perron 2 *
     1 University of Chicago
2 Universite' de Montre'al , CIREQ , CIRANO

* To whom correspondence should be addressed.
Benoit Perron, E-mail: benoit.perron{at}umontreal.ca


  Abstract

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.
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