Bias-Correcting the Realized Range-Based Variance in the Presence of Market Microstructure Noise

37 Pages Posted: 11 Oct 2006 Last revised: 6 Sep 2010

See all articles by Kim Christensen

Kim Christensen

Aarhus University - CREATES

Mark Podolskij

University of Heidelberg - Institute of Applied Mathematics

Mathias Vetter

Ruhr University of Bochum

Date Written: May 15, 2008

Abstract

Market microstructure noise is a challenge to high-frequency based estimation of the integrated variance, because the noise accumulates with the sampling frequency. This has lead to widespread use of constructing the realized variance, a sum of squared intraday returns, from sparsely sampled data, for example 5- or 15-minute returns. In this paper, we analyze the impact of microstructure noise on the realized range-based variance and propose a bias-correction to the range-statistic. The new estimator is shown to be consistent for the integrated variance and asymptotically mixed Gaussian under simple forms of microstructure noise. We can select an optimal partition of the high-frequency data in order to minimize its asymptotic conditional variance. The finite sample properties of our estimator are studied with Monte Carlo simulations and we implement it using Microsoft high-frequency data from TAQ. We find that a bias-corrected range-statistic often leads to much smaller confidence intervals for the integrated variance, relative to the realized variance.

Keywords: Bias-correction, Integrated variance, Market microstructure noise, Realized range-based variance, Realized variance

JEL Classification: C10, C80

Suggested Citation

Christensen, Kim and Podolskij, Mark and Vetter, Mathias, Bias-Correcting the Realized Range-Based Variance in the Presence of Market Microstructure Noise (May 15, 2008). Finance Stochastics, Vol. 13, No. 2, 2009. Available at SSRN: https://ssrn.com/abstract=935419 or http://dx.doi.org/10.2139/ssrn.935419

Kim Christensen

Aarhus University - CREATES ( email )

Department of Economics and Business Economics
Fuglesangs Allé 4
Aarhus V, 8210
Denmark

Mark Podolskij

University of Heidelberg - Institute of Applied Mathematics ( email )

Grabengasse 1
Heidelberg, 69117
Germany
00496221546276 (Phone)

Mathias Vetter (Contact Author)

Ruhr University of Bochum ( email )

Universitätsstraße 150
Bochum, NRW 44780
Germany

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