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

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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.

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Authors and Affiliations

  1. Nordea, Markets Division, Global Fixed Income Trading, Christiansbro, Strandgade 3, PO Box 850, 0900, Copenhagen C, Denmark

    Kim Christensen

  2. CREATES, University of Aarhus, School of Economics and Management, Building 1322, 8000, Aarhus C, Denmark

    Mark Podolskij

  3. Department of Probability and Statistics, Ruhr University of Bochum, Universitätstrasse 150, 44780, Bochum, Germany

    Mathias Vetter

Authors
  1. Kim Christensen
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  2. Mark Podolskij
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  3. Mathias Vetter
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Corresponding author

Correspondence to Kim Christensen.

Additional information

We should like to thank an anonymous referee and the associate editor for insightful comments on an earlier draft. Parts of this paper were written while Kim Christensen was at the University of California, San Diego, whose hospitality is gratefully acknowledged. Mark Podolskij received financial support from CREATES funded by the Danish National Research Foundation, and Mathias Vetter was supported by the Deutsche Forschungsgemeinschaft grant SFB 475 “Reduction of Complexity in Multivariate Data Structures.” The code for this paper was written in the Ox programming language, due to Doornik (2002). All views expressed here are those of the authors and do not necessarily represent the views of Nordea.

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Christensen, K., Podolskij, M. & Vetter, M. Bias-correcting the realized range-based variance in the presence of market microstructure noise. Finance Stoch 13, 239–268 (2009). https://doi.org/10.1007/s00780-009-0089-9

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