A Fundamentally Different Interpretation of the Relation between Implied and Realized Volatility

We argue that the persistence properties of financial market volatility need to be taken into account when carrying out inference about volatility measures, for example when assessing the relation between realized and implied volatility series. If these volatility measures display long memory, as often argued in recent work, then the conventional predictive regression between implied volatility (regressor) and realized volatility over the remaining life of the option (regressand) appears to be a (fractional) cointegrating relation. Since cointegration is associated with long-run comovements, this finding modifies the usual interpretation of such regression as a study towards assessing option market efficiency (based on a certain option pricing model) and/or short-term unbiasedness of implied volatility as a predictor of realized volatility. In this paper we use spectral methods and exploit the potential long memory in the data to design an econometric methodology which is robust to the various issues that the literature on the relation between implied and realized volatility has proposed as plausible explanations (measurement errors and presence of an unobservable time-varying risk premium, for instance) for an estimated slope coefficient less than one, implying biasedness, in the standard predictive regression. Our evidence in favor of long-run unbiasedness is rather strong. Little can be said about market efficiency and/or short-term unbiasedness which were the objects of the previous studies.