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Estimating quadratic variation when quoted prices change by a constant increment

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  • Large, Jeremy

Abstract

For financial assets whose best quotes almost always change by jumping by the market's price tick size (one cent, five cents, etc.), this paper proposes an estimator of Quadratic Variation which controls for microstructure effects. It measures the prevalence of alternations, where quotes jump back to their just-previous price. It defines a simple property called "uncorrelated alternation", which under conditions implies that the estimator is consistent in an asymptotic limit theory, where jumps become very frequent and small. Feasible limit theory is developed, and in simulations works well.

Suggested Citation

  • Large, Jeremy, 2011. "Estimating quadratic variation when quoted prices change by a constant increment," Journal of Econometrics, Elsevier, vol. 160(1), pages 2-11, January.
  • Handle: RePEc:eee:econom:v:160:y:2011:i:1:p:2-11
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    Citations

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    Cited by:

    1. Hansen, Peter Reinhard, 2015. "A martingale decomposition of discrete Markov chains," Economics Letters, Elsevier, vol. 133(C), pages 14-18.
    2. Kalnina, Ilze & Linton, Oliver, 2008. "Estimating quadratic variation consistently in the presence of endogenous and diurnal measurement error," Journal of Econometrics, Elsevier, vol. 147(1), pages 47-59, November.
    3. Yingying Li & Per A. Mykland, 2007. "Are volatility estimators robust with respect to modeling assumptions?," Papers 0709.0440, arXiv.org.
    4. Julius Bonart & Fabrizio Lillo, 2016. "A continuous and efficient fundamental price on the discrete order book grid," Papers 1608.00756, arXiv.org, revised Aug 2016.
    5. Patton, Andrew J. & Sheppard, Kevin, 2009. "Optimal combinations of realised volatility estimators," International Journal of Forecasting, Elsevier, vol. 25(2), pages 218-238.
    6. 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.
    7. Patton, Andrew J., 2011. "Data-based ranking of realised volatility estimators," Journal of Econometrics, Elsevier, vol. 161(2), pages 284-303, April.
    8. Li, Yingying & Xie, Shangyu & Zheng, Xinghua, 2016. "Efficient estimation of integrated volatility incorporating trading information," Journal of Econometrics, Elsevier, vol. 195(1), pages 33-50.

    More about this item

    Keywords

    Realized volatility Realized variance Quadratic variation Market microstructure High-frequency data Pure jump process;

    JEL classification:

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

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