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

Author

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  • Aymen Jedidi

    (FiQuant - Chaire de finance quantitative - MICS - Mathématiques et Informatique pour la Complexité et les Systèmes - CentraleSupélec, MAS - Mathématiques Appliquées aux Systèmes - EA 4037 - Ecole Centrale Paris)

  • Frédéric Abergel

    (FiQuant - Chaire de finance quantitative - MICS - Mathématiques et Informatique pour la Complexité et les Systèmes - CentraleSupélec, MAS - Mathématiques Appliquées aux Systèmes - EA 4037 - Ecole Centrale Paris)

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.

Suggested Citation

  • Aymen Jedidi & Frédéric Abergel, 2013. "Stability and price scaling limit of a Hawkes-process based order book model," Working Papers hal-00821607, HAL.
  • Handle: RePEc:hal:wpaper:hal-00821607
    Note: View the original document on HAL open archive server: https://hal.science/hal-00821607
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    References listed on IDEAS

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    1. repec:hal:wpaper:hal-00777941 is not listed on IDEAS
    2. Ioane Muni Toke & Fabrizio Pomponio, 2012. "Modelling Trades-Through in a Limit Order Book Using Hawkes Processes," Post-Print hal-00745554, HAL.
    3. Rama Cont & Adrien De Larrard, 2012. "Order book dynamics in liquid markets: limit theorems and diffusion approximations," Papers 1202.6412, arXiv.org.
    4. Rama Cont & Adrien de Larrard, 2013. "Price Dynamics in a Markovian Limit Order Market," Post-Print hal-00552252, HAL.
    5. Toke, Ioane Muni & Pomponio, Fabrizio, 2012. "Modelling trades-through in a limit order book using hawkes processes," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 6, pages 1-23.
    6. 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.
    7. Emmanuel Bacry & Sylvain Delattre & Marc Hoffmann & Jean-François Muzy, 2013. "Modelling microstructure noise with mutually exciting point processes," Post-Print hal-01313995, HAL.
    8. E. Bacry & J. F Muzy, 2013. "Hawkes model for price and trades high-frequency dynamics," Papers 1301.1135, arXiv.org.
    9. Ban Zheng & Franc{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.
    10. Frédéric Abergel & Aymen Jedidi, 2013. "A Mathematical Approach To Order Book Modeling," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(05), pages 1-40.
    11. Frederic Abergel & Aymen Jedidi, 2010. "A Mathematical Approach to Order Book Modeling," Papers 1010.5136, arXiv.org, revised Mar 2013.
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    Citations

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    Cited by:

    1. Peng Wu & Marcello Rambaldi & Jean-Franc{c}ois Muzy & Emmanuel Bacry, 2019. "Queue-reactive Hawkes models for the order flow," Papers 1901.08938, arXiv.org.
    2. Peng Wu & Marcello Rambaldi & Jean-François Muzy & Emmanuel Bacry, 2023. "A single queue-reactive Hawkes model for the order flow," Post-Print hal-02409073, HAL.
    3. Massil Achab & Emmanuel Bacry & Jean-Franc{c}ois Muzy & Marcello Rambaldi, 2017. "Analysis of order book flows using a nonparametric estimation of the branching ratio matrix," Papers 1706.03411, arXiv.org.
    4. Frédéric Abergel, 2015. "Lyapunov function for a Hawkes process-based limit order book," Working Papers hal-01113533, HAL.
    5. José Da Fonseca & Riadh Zaatour, 2017. "Correlation and Lead–Lag Relationships in a Hawkes Microstructure Model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 37(3), pages 260-285, March.
    6. Emmanuel Bacry & Iacopo Mastromatteo & Jean-Franc{c}ois Muzy, 2015. "Hawkes processes in finance," Papers 1502.04592, arXiv.org, revised May 2015.
    7. Peng Wu & Marcello Rambaldi & Jean-François Muzy & Emmanuel Bacry, 2021. "Queue-reactive Hawkes models for the order flow," Working Papers hal-02409073, HAL.
    8. Xuefeng Gao & S. J. Deng, 2014. "Hydrodynamic limit of order book dynamics," Papers 1411.7502, arXiv.org, revised Feb 2016.

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    More about this item

    Keywords

    Order book; Hawkes process; diffusive limit;
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