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Quadratic Variation by Markov Chains

  • Peter Reinhard Hansen

    ()

    (Stanford University and CREATES)

  • Guillaume Horel

    (Merrill Lynch, New York)

We introduce a novel estimator of the quadratic variation that is based on the theory of Markov chains. The estimator is motivated by some general results concerning filtering contaminated semimartingales. Specifically, we show that filtering can in principle remove the effects of market microstructure noise in a general framework where little is assumed about the noise. For the practical implementation, we adopt the discrete Markov chain model that is well suited for the analysis of financial high-frequency prices. The Markov chain framework facilitates simple expressions and elegant analytical results. The proposed estimator is consistent with a Gaussian limit distribution and we study its properties in simulations and an empirical application.

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File URL: ftp://ftp.econ.au.dk/creates/rp/09/rp09_13.pdf
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Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2009-13.

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Length: 57
Date of creation: 24 Mar 2009
Date of revision:
Handle: RePEc:aah:create:2009-13
Contact details of provider: Web page: http://www.econ.au.dk/afn/

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  1. F. M. Bandi & J. R. Russell, 2008. "Microstructure Noise, Realized Variance, and Optimal Sampling," Review of Economic Studies, Oxford University Press, vol. 75(2), pages 339-369.
  2. Kim Christensen & Roel Oomen & Mark Podolskij, 2010. "Realised quantile-based estimation of the integrated variance," Post-Print hal-00732538, HAL.
  3. Nour Meddahi, 2002. "A theoretical comparison between integrated and realized volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 479-508.
  4. Zhou, Bin, 1996. "High-Frequency Data and Volatility in Foreign-Exchange Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 45-52, January.
  5. Neil Shephard & Ole E. Barndorff-Nielsen, 2006. "Subsampling realised kernels," Economics Series Working Papers 278, University of Oxford, Department of Economics.
  6. Jean Jacod & Yingying Li & Per A. Mykland & Mark Podolskij & Mathias Vetter, 2007. "Microstructure Noise in the Continuous Case: The Pre-Averaging Approach - JLMPV-9," CREATES Research Papers 2007-43, School of Economics and Management, University of Aarhus.
  7. Torben G. Andersen & Dobrislav Dobrev & Ernst Schaumburg, 2009. "Duration-Based Volatility Estimation," Global COE Hi-Stat Discussion Paper Series gd08-034, Institute of Economic Research, Hitotsubashi University.
  8. Christensen, Kim & Podolski, Mark, 2005. "Asymptotic theory for range-based estimation of integrated variance of a continuous semi-martingale," Technical Reports 2005,18, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
  9. repec:oxf:wpaper:264 is not listed on IDEAS
  10. Peter Hansen & Jeremy Large & Asger Lunde, 2008. "Moving Average-Based Estimators of Integrated Variance," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 79-111.
  11. John M. Maheu & Thomas H. McCurdy, 2002. "Nonlinear Features of Realized FX Volatility," The Review of Economics and Statistics, MIT Press, vol. 84(4), pages 668-681, November.
  12. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July.
  13. Jeremy Large, 2005. "Estimating quadratic variation when quoted prices jump by a constant increment," OFRC Working Papers Series 2005fe05, Oxford Financial Research Centre.
  14. Sílvia Gonçalves & Nour Meddahi, 2009. "Bootstrapping Realized Volatility," Econometrica, Econometric Society, vol. 77(1), pages 283-306, 01.
  15. Hansen, Peter R. & Lunde, Asger, 2006. "Realized Variance and Market Microstructure Noise," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 127-161, April.
  16. Lan Zhang & Per A. Mykland & Yacine Ait-Sahalia, 2003. "A Tale of Two Time Scales: Determining Integrated Volatility with Noisy High Frequency Data," NBER Working Papers 10111, National Bureau of Economic Research, Inc.
  17. Jim Griffin & Roel Oomen, 2008. "Sampling Returns for Realized Variance Calculations: Tick Time or Transaction Time?," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 230-253.
  18. Gonçalves, Sílvia & Meddahi, Nour, 2011. "Box-Cox transforms for realized volatility," Journal of Econometrics, Elsevier, vol. 160(1), pages 129-144, January.
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