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Improved volatility estimation based on limit order books

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  • Bibinger, Markus
  • Jirak, Moritz
  • Reiss, Markus

Abstract

For a semi-martingale Xt, which forms a stochastic boundary, a rate-optimal estimator for its quadratic variation (X;X)t is constructed based on observations in the vicinity of Xt. The problem is embedded in a Poisson point process framework, which reveals an interesting connection to the theory of Brownian excursion areas. A major application is the estimation of the integrated squared volatility of an effcient price process Xt from intra-day order book quotes. We derive n -1/3 as optimal convergence rate of integrated squared volatility estimation in a high-frequency framework with n observations (in mean). This considerably improves upon the classical n -1/4-rate obtained from transaction prices under microstructure noise.

Suggested Citation

  • Bibinger, Markus & Jirak, Moritz & Reiss, Markus, 2014. "Improved volatility estimation based on limit order books," SFB 649 Discussion Papers 2014-053, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2014-053
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    References listed on IDEAS

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    1. Thierry Foucault & Ohad Kadan & Eugene Kandel, 2005. "Limit Order Book as a Market for Liquidity," The Review of Financial Studies, Society for Financial Studies, vol. 18(4), pages 1171-1217.
    2. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Designing Realized Kernels to Measure the ex post Variation of Equity Prices in the Presence of Noise," Econometrica, Econometric Society, vol. 76(6), pages 1481-1536, November.
    3. Rama Cont & Adrien De Larrard, 2012. "Order book dynamics in liquid markets: limit theorems and diffusion approximations," Papers 1202.6412, arXiv.org.
    4. Jim Gatheral & Roel Oomen, 2010. "Zero-intelligence realized variance estimation," Finance and Stochastics, Springer, vol. 14(2), pages 249-283, April.
    5. Naes, Randi & Skjeltorp, Johannes A., 2006. "Order book characteristics and the volume-volatility relation: Empirical evidence from a limit order market," Journal of Financial Markets, Elsevier, vol. 9(4), pages 408-432, November.
    6. Jean-Philippe Bouchaud & Marc Mezard & Marc Potters, 2002. "Statistical properties of stock order books: empirical results and models," Quantitative Finance, Taylor & Francis Journals, vol. 2(4), pages 251-256.
    7. Rama Cont & Sasha Stoikov & Rishi Talreja, 2010. "A Stochastic Model for Order Book Dynamics," Operations Research, INFORMS, vol. 58(3), pages 549-563, June.
    8. Biais, Bruno & Hillion, Pierre & Spatt, Chester, 1995. "An Empirical Analysis of the Limit Order Book and the Order Flow in the Paris Bourse," Journal of Finance, American Finance Association, vol. 50(5), pages 1655-1689, December.
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    Cited by:

    1. Gwennaëlle Mabon, 2014. "Adaptive Deconvolution on the Nonnegative Real Line," Working Papers 2014-40, Center for Research in Economics and Statistics.

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    More about this item

    Keywords

    Brownian excursion area; limit order book; integrated volatility; Feynman-Kac; high-frequency data; Poisson point process;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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