Finance and Stochastics

, Volume 13, Issue 2, pp 239–268

Bias-correcting the realized range-based variance in the presence of market microstructure noise

Article

DOI: 10.1007/s00780-009-0089-9

Cite this article as:
Christensen, K., Podolskij, M. & Vetter, M. Finance Stoch (2009) 13: 239. doi:10.1007/s00780-009-0089-9

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 led 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 

Mathematics Subject Classification (2000)

62E20 62P20 

JEL Classification

C10 C80 

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Kim Christensen
    • 1
  • Mark Podolskij
    • 2
  • Mathias Vetter
    • 3
  1. 1.Nordea, Markets DivisionGlobal Fixed Income TradingCopenhagen CDenmark
  2. 2.CREATESUniversity of Aarhus, School of Economics and ManagementAarhus CDenmark
  3. 3.Department of Probability and StatisticsRuhr University of BochumBochumGermany

Personalised recommendations