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Volatility estimation based on extremes of the bridge (in Russian)

Author

Listed:
  • Svetlana Lapinova

    (Higher School of Economics, Nizhni Novgorod, Russia)

  • Alexander Saichev

    (Nizhni Novgorod State University, Russia
    Swiss Federal Institute of Technology, Zurich, Switzerland)

  • Maria Tarakanova

    (Nizhni Novgorod State University, Russia)

Abstract

We investigate properties of the volatility estimator, which is proportional to the square of oscillations of the bridge formed by the logarithm of the incremental price of a financial instrument at a specified time interval. In the framework of the geometric Brownian motion model for price increments we show by analytical computations and statistical simulations that the proposed volatility estimator by the bridge is much more efficient than the well-known Parkinson and Garman–Class estimators. We also discuss possible usages of the estimators for estimation of integrated volatility.

Suggested Citation

  • Svetlana Lapinova & Alexander Saichev & Maria Tarakanova, 2012. "Volatility estimation based on extremes of the bridge (in Russian)," Quantile, Quantile, issue 10, pages 73-90, December.
    • Handle: RePEc:qnt:quantl:y:2012:i:10:p:73-90
    as

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    References listed on IDEAS

    as
    1. Parkinson, Michael, 1980. "The Extreme Value Method for Estimating the Variance of the Rate of Return," The Journal of Business, University of Chicago Press, vol. 53(1), pages 61-65, January.
    2. Garman, Mark B & Klass, Michael J, 1980. "On the Estimation of Security Price Volatilities from Historical Data," The Journal of Business, University of Chicago Press, vol. 53(1), pages 67-78, January.
    3. A. Saichev & D. Sornette, 2012. "A simple microstructure return model explaining microstructure noise and Epps effects," Papers 1202.3915, arXiv.org.
    4. Robert Ślepaczuk & Grzegorz Zakrzewski, 2009. "High-Frequency and Model-Free Volatility Estimators," Working Papers 2009-13, Faculty of Economic Sciences, University of Warsaw.
    5. Martens, Martin & van Dijk, Dick, 2007. "Measuring volatility with the realized range," Journal of Econometrics, Elsevier, vol. 138(1), pages 181-207, May.
    6. A. Saichev & D. Sornette, 2011. "Time-Bridge Estimators of Integrated Variance," Papers 1108.2611, arXiv.org.
    7. Didier Sornette & Alexander I. Saichev, 2012. "A Simple Microstructure Return Model Explaining Microstructure Noise and Epps Effects," Swiss Finance Institute Research Paper Series 12-08, Swiss Finance Institute.
    8. Yannick Malevergne & Alex Saichev & Didier Sornette, 2010. "Theory of Zipf's Law and Beyond," Post-Print hal-01892766, HAL.
    9. Kunitomo, Naoto, 1992. "Improving the Parkinson Method of Estimating Security Price Volatilities," The Journal of Business, University of Chicago Press, vol. 65(2), pages 295-302, April.
    Full references (including those not matched with items on IDEAS)

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    Keywords

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    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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