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.

Keywords:

• range-based volatility
• realized range
• two-scales realized volatility
• volatility estimation
• high-frequency data

JEL Classification:

• C13
• C14

Notes

¹For a review of the extensive literature on realized volatility see McAleer and Medeiros (2008).

²A correction of the realized range for irregular sampling is proposed by Rossi and Spazzini (2009).

³An estimate of realized volatility at the 5 minute frequency comprises 102 returns for the market opening time from 9:00 am to 5:30 pm. When the asset is quoted every second, realized volatility can be computed based on the price observations at 9:00:00, 9:05:00 and so on. Alternatively, it can be established based on quotations at 9:00:01, 9:05:01 and so on. Similarly, 298 further volatility estimates can be obtained. Averaging across all 300 estimates leads to the low frequency variance .

⁴Results are not tabulated to save space but are available upon request.

⁵In such a context, it could also be interesting to use asymmetric loss functions as applied by Brailsford and Faff (1996) which penalize under(over)predictions more heavily. Utilization of these approach did not provide incremental insights and the corresponding results are omitted to save space.