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Stability and price scaling limit of a Hawkes-process based order book model

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Author Info

  • Aymen Jedidi

    ()
    (FiQuant - Chaire de finance quantitative - Ecole Centrale Paris, MAS - Mathématiques Appliquées aux Systèmes - EA 4037 - Ecole Centrale Paris)

  • Frédéric Abergel

    ()
    (FiQuant - Chaire de finance quantitative - Ecole Centrale Paris, MAS - Mathématiques Appliquées aux Systèmes - EA 4037 - Ecole Centrale Paris)

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    Abstract

    In this note, we cast a Hawkes process-based order book model into a markovian setting and; using techniques from the theory of Markov chains and stochastic stability, show that the order book is stable and leads to a diffusive price limit at large time scales.

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    File URL: http://hal.archives-ouvertes.fr/docs/00/82/16/07/PDF/HawkesTheo_HAL.pdf
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    Bibliographic Info

    Paper provided by HAL in its series Working Papers with number hal-00821607.

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    Date of creation: 2013
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    Handle: RePEc:hal:wpaper:hal-00821607

    Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00821607
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    Web page: http://hal.archives-ouvertes.fr/

    Related research

    Keywords: Order book; Hawkes process; diffusive limit;

    This paper has been announced in the following NEP Reports:

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    1. repec:hal:wpaper:hal-00777941 is not listed on IDEAS
    2. Ban Zheng & Fran\c{c}ois Roueff & Fr\'ed\'eric Abergel, 2013. "Ergodicity and scaling limit of a constrained multivariate Hawkes process," Papers 1301.5007, arXiv.org, revised Feb 2014.
    3. E. Bacry & S. Delattre & M. Hoffmann & J. F. Muzy, 2013. "Modelling microstructure noise with mutually exciting point processes," Quantitative Finance, Taylor & Francis Journals, vol. 13(1), pages 65-77, January.
    4. E. Bacry & J. F Muzy, 2013. "Hawkes model for price and trades high-frequency dynamics," Papers 1301.1135, arXiv.org.
    5. Frederic Abergel & Aymen Jedidi, 2010. "A Mathematical Approach to Order Book Modeling," Papers 1010.5136, arXiv.org, revised Mar 2013.
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