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A New Approach for the Dynamics of Ultra-High-Frequency Data: The Model with Uncertainty Zones


  • Christian Y. Robert
  • Mathieu Rosenbaum


In this paper, we provide a model which accommodates the assumption of a continuous efficient price with the inherent properties of ultra-high-frequency transaction data (price discreteness, irregular temporal spacing, diurnal patterns...). Our approach consists in designing a stochastic mechanism for deriving the transaction prices from the latent efficient price. The main idea behind the model is that, if a transaction occurs at some value on the tick grid and leads to a price change, then the efficient price has been close enough to this value shortly before the transaction. We call uncertainty zones the bands around the mid-tick grid where the efficient price is too far from the tick grid to trigger a price change. In our setting, the width of these uncertainty zones quantifies the aversion to price changes of the market participants. Furthermore, this model enables us to derive approximated values of the efficient price at some random times, which is particularly useful for building statistical procedures. Convincing results are obtained through a simulation study and the use of the model over 10 representative stocks. Copyright The Author 2010. Published by Oxford University Press. All rights reserved. For permissions, please e-mail:, Oxford University Press.

Suggested Citation

  • Christian Y. Robert & Mathieu Rosenbaum, 2011. "A New Approach for the Dynamics of Ultra-High-Frequency Data: The Model with Uncertainty Zones," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 9(2), pages 344-366, Spring.
  • Handle: RePEc:oup:jfinec:v:9:y:2011:i:2:p:344-366

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    Cited by:

    1. Charles-Albert Lehalle, 2013. "Market Microstructure Knowledge Needed for Controlling an Intra-Day Trading Process," Papers 1302.4592,
    2. Potiron, Yoann & Mykland, Per A., 2017. "Estimation of integrated quadratic covariation with endogenous sampling times," Journal of Econometrics, Elsevier, vol. 197(1), pages 20-41.
    3. Bacry, E. & Delattre, S. & Hoffmann, M. & Muzy, J.F., 2013. "Some limit theorems for Hawkes processes and application to financial statistics," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2475-2499.
    4. Rama Cont & Adrien De Larrard, 2013. "Price Dynamics in a Markovian Limit Order Market," Post-Print hal-00552252, HAL.
    5. Pietro Fodra & Huy^en Pham, 2013. "High frequency trading and asymptotics for small risk aversion in a Markov renewal model," Papers 1310.1756,, revised Jan 2015.
    6. Aim'e Lachapelle & Jean-Michel Lasry & Charles-Albert Lehalle & Pierre-Louis Lions, 2013. "Efficiency of the Price Formation Process in Presence of High Frequency Participants: a Mean Field Game analysis," Papers 1305.6323,, revised Aug 2015.
    7. Simon Clinet & Yoann Potiron, 2017. "Efficient asymptotic variance reduction when estimating volatility in high frequency data," Papers 1701.01185,, revised Jul 2017.
    8. repec:eee:dyncon:v:79:y:2017:i:c:p:154-183 is not listed on IDEAS
    9. Thibault Jaisson, 2015. "Liquidity and Impact in Fair Markets," Papers 1506.02507,
    10. Jim Gatheral & Thibault Jaisson & Mathieu Rosenbaum, 2014. "Volatility is rough," Papers 1410.3394,
    11. Weibing Huang & Charles-Albert Lehalle & Mathieu Rosenbaum, 2015. "Simulating and Analyzing Order Book Data: The Queue-Reactive Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 107-122, March.
    12. Pietro Fodra & Huyen Pham, 2013. "High frequency trading in a Markov renewal model," Working Papers hal-00867113, HAL.
    13. Weibing Huang & Charles-Albert Lehalle & Mathieu Rosenbaum, 2015. "How to predict the consequences of a tick value change? Evidence from the Tokyo Stock Exchange pilot program," Papers 1507.07052,
    14. Aurélien Alfonsi & Pierre Blanc, 2016. "Dynamic optimal execution in a mixed-market-impact Hawkes price model," Finance and Stochastics, Springer, vol. 20(1), pages 183-218, January.
    15. Julius Bonart & Fabrizio Lillo, 2016. "A continuous and efficient fundamental price on the discrete order book grid," Papers 1608.00756,, revised Aug 2016.
    16. Aurélien Alfonsi & Pierre Blanc, 2016. "Dynamic optimal execution in a mixed-market-impact Hawkes price model," Finance and Stochastics, Springer, vol. 20(1), pages 183-218, January.
    17. Aur'elien Alfonsi & Pierre Blanc, 2014. "Dynamic optimal execution in a mixed-market-impact Hawkes price model," Papers 1404.0648,, revised Jun 2015.
    18. Yoann Potiron & Per Mykland, 2016. "Local Parametric Estimation in High Frequency Data," Papers 1603.05700,, revised Mar 2017.
    19. Gianbiagio Curato & Fabrizio Lillo, 2013. "Modeling the coupled return-spread high frequency dynamics of large tick assets," Papers 1310.4539,
    20. Aurélien Alfonsi & Pierre Blanc, 2016. "Dynamic optimal execution in a mixed-market-impact Hawkes price model," Post-Print hal-00971369, HAL.
    21. Khalil Dayri & Mathieu Rosenbaum, 2012. "Large tick assets: implicit spread and optimal tick size," Papers 1207.6325,, revised Jan 2013.

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