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Time-Bridge Estimators of Integrated Variance

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  • A. Saichev
  • D. Sornette

Abstract

We present a set of log-price integrated variance estimators, equal to the sum of open-high-low-close bridge estimators of spot variances within $n$ subsequent time-step intervals. The main characteristics of some of the introduced estimators is to take into account the information on the occurrence times of the high and low values. The use of the high's and low's of the bridge associated with the original process makes the estimators significantly more efficient that the standard realized variance estimators and its generalizations. Adding the information on the occurrence times of the high and low values improves further the efficiency of the estimators, much above those of the well-known realized variance estimator and those derived from the sum of Garman and Klass spot variance estimators. The exact analytical results are derived for the case where the underlying log-price process is an It\^o stochastic process. Our results suggests more efficient ways to record financial prices at intermediate frequencies.

Suggested Citation

  • A. Saichev & D. Sornette, 2011. "Time-Bridge Estimators of Integrated Variance," Papers 1108.2611, arXiv.org.
    • Handle: RePEc:arx:papers:1108.2611
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    References listed on IDEAS

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    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. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    4. Alexander Saichev & Didier Sornette & Vladimir Filimonov & Fulvio Corsi, 2009. "Homogeneous Volatility Bridge Estimators," Papers 0912.1617, arXiv.org.
    5. Alexander SAICHEV & Didier SORNETTE & Vladimir FILIMONOV & Fulvio CORSI, 2009. "Homogeneous Volatility Bridge Estimators," Swiss Finance Institute Research Paper Series 09-46, Swiss Finance Institute.
    6. Jain, Satish (ed.), 2010. "Law and Economics," OUP Catalogue, Oxford University Press, number 9780198067733.
    7. Zhang, Lan & Mykland, Per A. & Ait-Sahalia, Yacine, 2005. "A Tale of Two Time Scales: Determining Integrated Volatility With Noisy High-Frequency Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1394-1411, December.
    8. Yacine Aït-Sahalia, 2005. "How Often to Sample a Continuous-Time Process in the Presence of Market Microstructure Noise," The Review of Financial Studies, Society for Financial Studies, vol. 18(2), pages 351-416.
    9. Alex Saichev & Yannick Malevergne & Didier Sornette, 2010. "Theory of Zipf's Law and Beyond," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-642-02946-2, October.
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    Cited by:

    1. 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.

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