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

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  • Kim Christensen
  • Mark Podolskij
  • Mathias Vetter

Abstract

Market microstructure noise is a challenge to high-frequency based estimation of the integrated variance, because the noise accumulates with the sampling frequency. In this paper, we analyze the impact of microstructure noise on the realized range-based variance and propose a bias-correction to the rangestatistic. The new estimator is shown to be consistent for the integrated variance and asymptotically mixed Gaussian under simple forms of microstructure noise, and 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 on high-frequency data from TAQ. We find that a bias-corrected range-statistic often has much smaller confidence intervals than the realized variance.
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  • Kim Christensen & Mark Podolskij & Mathias Vetter, 2009. "Bias-correcting the realized range-based variance in the presence of market microstructure noise," Finance and Stochastics, Springer, vol. 13(2), pages 239-268, April.
    • Handle: RePEc:spr:finsto:v:13:y:2009:i:2:p:239-268
    DOI: 10.1007/s00780-009-0089-9
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    Cited by:

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    2. Yuta Kurose, 2021. "Stochastic volatility model with range-based correction and leverage," Papers 2110.00039, arXiv.org, revised Oct 2021.
    3. Massimiliano Caporin & Eduardo Rossi & Paolo Santucci de Magistris, 2016. "Volatility Jumps and Their Economic Determinants," Journal of Financial Econometrics, Oxford University Press, vol. 14(1), pages 29-80.
    4. Massimiliano Caporin & Eduardo Rossi & Paolo Santucci de Magistris, 2011. "Conditional jumps in volatility and their economic determinants," "Marco Fanno" Working Papers 0138, Dipartimento di Scienze Economiche "Marco Fanno".
    5. Beatriz Vaz de Melo Mendes & Victor Bello Accioly, 2017. "Improving (E)GARCH forecasts with robust realized range measures: Evidence from international markets," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 41(4), pages 631-658, October.
    6. Wu, Chih-Chiang & Chiu, Junmao, 2017. "Economic evaluation of asymmetric and price range information in gold and general financial markets," Journal of International Money and Finance, Elsevier, vol. 74(C), pages 53-68.
    7. Liu, Qiang & Liu, Yiqi & Liu, Zhi & Wang, Li, 2018. "Estimation of spot volatility with superposed noisy data," The North American Journal of Economics and Finance, Elsevier, vol. 44(C), pages 62-79.
    8. Zhanglong Wang & Kent Wang & Zheyao Pan, 2015. "Conditional equity risk premia and realized variance jump risk," Australian Journal of Management, Australian School of Business, vol. 40(2), pages 295-317, May.
    9. Massimiliano Caporin & Gabriel G. Velo, 2011. "Modeling and forecasting realized range volatility," "Marco Fanno" Working Papers 0128, Dipartimento di Scienze Economiche "Marco Fanno".
    10. Robert Azencott & Peng Ren & Ilya Timofeyev, 2020. "Realised volatility and parametric estimation of Heston SDEs," Finance and Stochastics, Springer, vol. 24(3), pages 723-755, July.
    11. Luca Barbaglia & Christophe Croux & Ines Wilms, 2017. "Volatility spillovers and heavy tails: a large t-Vector AutoRegressive approach," Working Papers of Department of Decision Sciences and Information Management, Leuven 590528, KU Leuven, Faculty of Economics and Business (FEB), Department of Decision Sciences and Information Management, Leuven.
    12. Bannouh, Karim & Martens, Martin & van Dijk, Dick, 2013. "Forecasting volatility with the realized range in the presence of noise and non-trading," The North American Journal of Economics and Finance, Elsevier, vol. 26(C), pages 535-551.
    13. Neda Todorova, 2012. "Volatility estimators based on daily price ranges versus the realized range," Applied Financial Economics, Taylor & Francis Journals, vol. 22(3), pages 215-229, February.
    14. Caporin, Massimiliano & Velo, Gabriel G., 2015. "Realized range volatility forecasting: Dynamic features and predictive variables," International Review of Economics & Finance, Elsevier, vol. 40(C), pages 98-112.
    15. Fangfang Wang, 2016. "An Unbiased Measure of Integrated Volatility in the Frequency Domain," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(2), pages 147-164, March.
    16. Gong, Xu & Lin, Boqiang, 2018. "Structural changes and out-of-sample prediction of realized range-based variance in the stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 27-39.
    17. Filip Zikes, 2017. "Measuring Transaction Costs in the Absence of Timestamps," Finance and Economics Discussion Series 2017-045, Board of Governors of the Federal Reserve System (U.S.).
    18. Chen, Wei-Peng & Choudhry, Taufiq & Wu, Chih-Chiang, 2013. "The extreme value in crude oil and US dollar markets," Journal of International Money and Finance, Elsevier, vol. 36(C), pages 191-210.
    19. Kalnina, Ilze, 2011. "Subsampling high frequency data," Journal of Econometrics, Elsevier, vol. 161(2), pages 262-283, April.
    20. Wu, Chih-Chiang & Liang, Shin-Shun, 2011. "The economic value of range-based covariance between stock and bond returns with dynamic copulas," Journal of Empirical Finance, Elsevier, vol. 18(4), pages 711-727, September.

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    More about this item

    Keywords

    Bias correction; Integrated variance; Market microstructure noise; Realized range-based variance; Realized variance; 62E20; 62P20; C10; C80;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C80 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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