Long Memory and the Relation between Implied and Realized Volatility

Posted: 2 Apr 2008

See all articles by Federico M. Bandi

Federico M. Bandi

Johns Hopkins University - Carey Business School

Benoit Perron

University of Montreal - Department of Economics; Center for Interuniversity Research and Analysis on Organization (CIRANO); University of Montreal - Center for Interuniversity Research in Econometrics

Date Written: 2006

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

Suggested Citation

Bandi, Federico Maria and Perron, Benoit, Long Memory and the Relation between Implied and Realized Volatility ( 2006). Journal of Financial Econometrics, Vol. 4, Issue 4, pp. 636-670, 2006. Available at SSRN: https://ssrn.com/abstract=1115052 or http://dx.doi.org/10.1093/jjfinec/nbl003

Federico Maria Bandi (Contact Author)

Johns Hopkins University - Carey Business School ( email )

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Benoit Perron

University of Montreal - Department of Economics ( email )

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Center for Interuniversity Research and Analysis on Organization (CIRANO) ( email )

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Montreal H3A 2M8, Quebec
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University of Montreal - Center for Interuniversity Research in Econometrics ( email )

C.P. 6128, Succursale Centre-ville
Montreal, Quebec H3C 3J7
Canada

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