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Homogeneous Volatility Bridge Estimators

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  • Alexander Saichev
  • Didier Sornette
  • Vladimir Filimonov
  • Fulvio Corsi

Abstract

We present a theory of homogeneous volatility bridge estimators for log-price stochastic processes. The main tool of our theory is the parsimonious encoding of the information contained in the open, high and low prices of incomplete bridge, corresponding to given log-price stochastic process, and in its close value, for a given time interval. The efficiency of the new proposed estimators is favorably compared with that of the Garman-Klass and Parkinson estimators.

Suggested Citation

  • Alexander Saichev & Didier Sornette & Vladimir Filimonov & Fulvio Corsi, 2009. "Homogeneous Volatility Bridge Estimators," Papers 0912.1617, arXiv.org.
    • Handle: RePEc:arx:papers:0912.1617
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    References listed on IDEAS

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    1. A. Saichev & D. Sornette & V. Filimonov, 2009. "Most Efficient Homogeneous Volatility Estimators," Papers 0908.1677, arXiv.org.
    2. 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.
    3. A. Saichev & D. Sornette & V. Filimonov, "undated". "Most Efficient Homogeneous Volatility Estimators," Working Papers CCSS-09-007, ETH Zurich, Chair of Systems Design.
    4. 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.
    5. 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.
    6. 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.
    7. Fulvio Corsi & Gilles Zumbach & Ulrich A. Muller & Michel M. Dacorogna, 2001. "Consistent High-precision Volatility from High-frequency Data," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 30(2), pages 183-204, July.
    8. 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.
    9. Alexander I. SAICHEV & Didier SORNETTE & Vladimir FILIMONOV, 2009. "Most Efficient Homogeneous Volatility Estimators," Swiss Finance Institute Research Paper Series 09-35, Swiss Finance Institute.
    10. Donald MacKenzie, 2006. "An Engine, Not a Camera: How Financial Models Shape Markets," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262134608, December.
    11. Yang, Dennis & Zhang, Qiang, 2000. "Drift-Independent Volatility Estimation Based on High, Low, Open, and Close Prices," The Journal of Business, University of Chicago Press, vol. 73(3), pages 477-491, July.
    12. Chan, Leo & Lien, Donald, 2003. "Using high, low, open, and closing prices to estimate the effects of cash settlement on futures prices," International Review of Financial Analysis, Elsevier, vol. 12(1), pages 35-47.
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    1. A. Saichev & D. Sornette, 2011. "Time-Bridge Estimators of Integrated Variance," Papers 1108.2611, arXiv.org.

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