The Empirical Performance of Alternative Extreme Value Volatility Estimators

This paper addresses the following issue: given a set of daily observations on an asset (historical opening, closing, high and low prices), how should one go about estimating the asset’s volatility? We use high-frequency data on very liquid assets to construct daily realized volatility series, which enables us to treat volatility as observed rather than latent. We then compare the empirical performance of various estimators of asset return volatility against the realized volatility benchmark. This procedure makes it possible, for the first time, to study the bias and relative efficiency of the various estimators directly. The stock index results give overwhelming support to the use of extreme value volatility estimators, but the futures and currency results are less clear. We highlight a number of important instances in which extreme value volatility estimators are both less biased and more efficient than the traditional estimator. JEL Classification Codes: C14, C53, F31.