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


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  • Christian Y. Robert
  • Mathieu Rosenbaum
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    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.

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    Bibliographic Info

    Article provided by Society for Financial Econometrics in its journal Journal of Financial Econometrics.

    Volume (Year): 9 (2011)
    Issue (Month): 2 (Spring)
    Pages: 344-366

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    Handle: RePEc:oup:jfinec:v:9:y:2011:i:2:p:344-366

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    Cited by:
    1. Aurélien Alfonsi & Pierre Blanc, 2014. "Dynamic optimal execution in a mixed-market-impact Hawkes price model," Working Papers, HAL hal-00971369, HAL.
    2. Weibing Huang & Charles-Albert Lehalle & Mathieu Rosenbaum, 2013. "Simulating and analyzing order book data: The queue-reactive model," Papers, 1312.0563,, revised Sep 2014.
    3. Gianbiagio Curato & Fabrizio Lillo, 2013. "Modeling the coupled return-spread high frequency dynamics of large tick assets," Papers, 1310.4539,
    4. Khalil Dayri & Mathieu Rosenbaum, 2012. "Large tick assets: implicit spread and optimal tick size," Papers, 1207.6325,, revised Jan 2013.
    5. 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 Mar 2014.
    6. Charles-Albert Lehalle, 2013. "Market Microstructure Knowledge Needed for Controlling an Intra-Day Trading Process," Papers, 1302.4592,
    7. Pietro Fodra & Huy\^en Pham, 2013. "High frequency trading in a Markov renewal model," Papers, 1310.1756,
    8. Pietro Fodra & Huyen Pham, 2013. "High frequency trading in a Markov renewal model," Working Papers, HAL hal-00867113, HAL.
    9. 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, Elsevier, vol. 123(7), pages 2475-2499.
    10. Rama Cont & Adrien De Larrard, 2013. "Price Dynamics in a Markovian Limit Order Market," Post-Print, HAL hal-00552252, HAL.
    11. Aur\'elien Alfonsi & Pierre Blanc, 2014. "Dynamic optimal execution in a mixed-market-impact Hawkes price model," Papers, 1404.0648,


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