Realised Quantile-Based Estimation of the Integrated Variance

54 Pages Posted: 21 Jan 2008 Last revised: 29 Oct 2010

See all articles by Kim Christensen

Kim Christensen

Aarhus University - CREATES

Roel C. A. Oomen

Deutsche Bank AG (London); London School of Economics & Political Science (LSE) - Department of Statistics

Mark Podolskij

University of Heidelberg - Institute of Applied Mathematics

Date Written: September 1, 2009

Abstract

In this paper we propose a new jump robust measure of ex-post return variation that can be computed using potentially noisy data. The estimator exploits the link between return quantiles and volatility and is consistent for the integrated (diffusive) variance under weak conditions on the price process. We present various central limit theorems which show that the estimator converges at the best attainable rate and has excellent efficiency. Asymptotically, the estimator is immune to finite activity jumps and simulations show that also in finite sample it has superior robustness properties. In modified form, the estimator is applicable with market micro-structure noise and therefore operational on high frequency data. As such, it constitutes an appealing alternative to the existing jump-robust or noise-corrected realised variance measures. An empirical application using low and high frequency data is included to further illustrate the properties of the estimator.

Keywords: Finite activity jumps, Integrated variance, Market micro-structure noise, Order statistics, Realised variance

JEL Classification: C10, C80

Suggested Citation

Christensen, Kim and Oomen, Roel C.A. and Podolskij, Mark, Realised Quantile-Based Estimation of the Integrated Variance (September 1, 2009). Journal of Econometrics, Vol 159, No. 1, pp. 74-98, 2010. Available at SSRN: https://ssrn.com/abstract=1085553

Kim Christensen

Aarhus University - CREATES ( email )

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

Roel C.A. Oomen (Contact Author)

Deutsche Bank AG (London) ( email )

Winchester House
1 Great Winchester Street
London, EC2N 2DB
United Kingdom

London School of Economics & Political Science (LSE) - Department of Statistics ( email )

Houghton Street
London, England WC2A 2AE
United Kingdom

Mark Podolskij

University of Heidelberg - Institute of Applied Mathematics ( email )

Grabengasse 1
Heidelberg, 69117
Germany
00496221546276 (Phone)

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