Long Memory and the Relation Between Implied and Realized Volatility

We argue that the predictive regression between implied volatility (regressor) and re-alized volatility over the remaining life of a European option (regressand) is likely to be a fractional cointegrating relation. Since cointegration is associated with long-run co-movements, 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. Exploiting fractional cointegration and using narrow band spectral methods, we provide consistent es-timates 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. This result is in contrast with much existing work where the use of ordi-nary least squares methods leads to inconsistent (and downward biased) slope estimates. We find that, while 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. JEL classification: G13, G14, C53.