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Improved Volatility Estimation Based On Limit Order Books

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  • Markus Bibinger
  • Moritz Jirak
  • Markus Reiss

Abstract

For a semi-martingale Xt, which forms a stochastic boundary, a rate-optimal estimator for its quadratic variation hX;Xit is con- structed 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 ar- eas. A major application is the estimation of the integrated squared volatility of an ecient 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 classi- cal n􀀀1=4-rate obtained from transaction prices under microstructure noise.

Suggested Citation

  • Markus Bibinger & Moritz Jirak & Markus Reiss, 2014. "Improved Volatility Estimation Based On Limit Order Books," SFB 649 Discussion Papers SFB649DP2014-053, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    • Handle: RePEc:hum:wpaper:sfb649dp2014-053
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    References listed on IDEAS

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    5. 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.
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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:

    • Q42 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy - - - Alternative Energy Sources
    • Q47 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy - - - Energy Forecasting

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