IDEAS home Printed from https://ideas.repec.org/a/qnt/quantl/y2012i10p73-90.html
   My bibliography  Save this article

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

    Download full text from publisher

    File URL: http://quantile.ru/10/10-LS.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. A. Saichev & D. Sornette, 2012. "A simple microstructure return model explaining microstructure noise and Epps effects," Papers 1202.3915, arXiv.org.
    3. Martens, Martin & van Dijk, Dick, 2007. "Measuring volatility with the realized range," Journal of Econometrics, Elsevier, vol. 138(1), pages 181-207, May.
    4. 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.
    5. Yannick Malevergne & Alex Saichev & Didier Sornette, 2010. "Theory of Zipf's Law and Beyond," Post-Print hal-01892766, HAL.
    6. A. Saichev & D. Sornette, 2011. "Time-Bridge Estimators of Integrated Variance," Papers 1108.2611, arXiv.org.
    7. 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.
    8. Robert Ślepaczuk & Grzegorz Zakrzewski, 2009. "High-Frequency and Model-Free Volatility Estimators," Working Papers 2009-13, Faculty of Economic Sciences, University of Warsaw.
    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)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Chou, Ray Yeutien & Liu, Nathan, 2010. "The economic value of volatility timing using a range-based volatility model," Journal of Economic Dynamics and Control, Elsevier, vol. 34(11), pages 2288-2301, November.
    3. Christensen, Kim & Podolskij, Mark, 2007. "Realized range-based estimation of integrated variance," Journal of Econometrics, Elsevier, vol. 141(2), pages 323-349, December.
    4. Haibin Xie & Shouyang Wang, 2018. "Timing the market: the economic value of price extremes," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 4(1), pages 1-24, December.
    5. Yuta Kurose, 2021. "Stochastic volatility model with range-based correction and leverage," Papers 2110.00039, arXiv.org, revised Oct 2021.
    6. Caporin, Massimiliano & Ranaldo, Angelo & Santucci de Magistris, Paolo, 2013. "On the predictability of stock prices: A case for high and low prices," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 5132-5146.
    7. Bertrand B. Maillet & Jean-Philippe R. M�decin, 2010. "Extreme Volatilities, Financial Crises and L-moment Estimations of Tail-indexes," Working Papers 2010_10, Department of Economics, University of Venice "Ca' Foscari".
    8. Hallin, Marc & La Vecchia, Davide, 2020. "A Simple R-estimation method for semiparametric duration models," Journal of Econometrics, Elsevier, vol. 218(2), pages 736-749.
    9. Igor Kliakhandler, 2007. "Execution edge of pit traders and intraday price ranges of soft commodities," Applied Financial Economics, Taylor & Francis Journals, vol. 17(5), pages 343-350.
    10. Gerlach, Richard & Wang, Chao, 2020. "Semi-parametric dynamic asymmetric Laplace models for tail risk forecasting, incorporating realized measures," International Journal of Forecasting, Elsevier, vol. 36(2), pages 489-506.
    11. 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.
    12. Liao, Yin & Anderson, Heather M., 2019. "Testing for cojumps in high-frequency financial data: An approach based on first-high-low-last prices," Journal of Banking & Finance, Elsevier, vol. 99(C), pages 252-274.
    13. Hiroyuki Kawakatsu, 2021. "Information in daily data volatility measurements," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(2), pages 1642-1656, April.
    14. Thierry Chauveau & Sylvain Friederich & Jérôme Héricourt & Emmanuel Jurczenko & Catherine Lubochinsky & Bertrand Maillet & Christophe Moussu & Bogdan Négréa & Hélène Raymond-Feingold, 2004. "La volatilité des marchés augmente-t-elle ?," Revue d'Économie Financière, Programme National Persée, vol. 74(1), pages 17-44.
    15. Alia Afzal & Philipp Sibbertsen, 2021. "Modeling fractional cointegration between high and low stock prices in Asian countries," Empirical Economics, Springer, vol. 60(2), pages 661-682, February.
    16. Lapinova, S. & Saichev, A. & Tarakanova, M., 2013. "Efficiency and probabilistic properties of bridge volatility estimator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(6), pages 1439-1451.
    17. Chao Wang & Richard Gerlach, 2019. "Semi-parametric Realized Nonlinear Conditional Autoregressive Expectile and Expected Shortfall," Papers 1906.09961, arXiv.org.
    18. Richard Gerlach & Declan Walpole & Chao Wang, 2017. "Semi-parametric Bayesian tail risk forecasting incorporating realized measures of volatility," Quantitative Finance, Taylor & Francis Journals, vol. 17(2), pages 199-215, February.
    19. Christensen, Kim & Podolskij, Mark, 2006. "Range-Based Estimation of Quadratic Variation," Technical Reports 2006,37, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    20. Sutton, Maxwell & Vasnev, Andrey L. & Gerlach, Richard, 2019. "Mixed interval realized variance: A robust estimator of stock price volatility," Econometrics and Statistics, Elsevier, vol. 11(C), pages 43-62.

    More about this item

    Keywords

    volatility; volatility estimators; efficiency; bias; extremes of Brownian motion;
    All these keywords.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:qnt:quantl:y:2012:i:10:p:73-90. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Stanislav Anatolyev (email available below). General contact details of provider: http://quantile.ru/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.