Volatility estimators based on daily price ranges versus the realized range

Abstract

This study investigates the relative performance of alternative extreme-value volatility estimators based on daily and intraday ranges of the German index DAX 30. As a benchmark, the two-scales realized volatility is used. Intraday data from 6 years and 4 months are divided into two periods of different liquidity and volatility levels. The empirical results show that all range-based estimators are superior compared to the classical estimator but are negatively biased due to the discreteness of the price process. The estimation accuracy of all volatility proxies depends on the drift of the price process. The performance of the estimators based on daily price ranges is furthermore very sensitive to the level of volatility. The realized range, an estimator obtained from intraday ranges is more efficient and less biased than the daily ranges. The main determinant of its properties appears to be the liquidity level. The adjustments according to Christensen and Podolskij (2007) and Martens and van Dijk (2007) perform significantly better than the Parkinson estimator and thus provide conclusive support for the relative advantage of the realized range for measuring equity index volatility.