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Limit order book modelling with high dimensional Hawkes processes

Author

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  • Xiaofei Lu

    (MICS - Mathématiques et Informatique pour la Complexité et les Systèmes - CentraleSupélec)

  • Frédéric Abergel

    (MICS - Mathématiques et Informatique pour la Complexité et les Systèmes - CentraleSupélec)

Abstract

The quality of various Hawkes-process-based order book models are assessed using some objective criteria. We start with a precise empirical analysis of the dependencies between order arrivals of various types, then, models built from multivariate, possibly nonlinear, Hawkes processes with multiple exponential kernels are introduced. Models are evaluated based on the distribution of forward recurrence times and the signature plot. This approach allows us to discriminate between various Hawkes-process- based models, and provide a financial interpretation of the more successful ones in terms of their behaviour at various time scales, and the presence of inhibition as well as excitation effects.

Suggested Citation

  • Xiaofei Lu & Frédéric Abergel, 2017. "Limit order book modelling with high dimensional Hawkes processes," Working Papers hal-01512430, HAL.
    • Handle: RePEc:hal:wpaper:hal-01512430
    Note: View the original document on HAL open archive server: https://hal.science/hal-01512430
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    References listed on IDEAS

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    1. Emmanuel Bacry & Iacopo Mastromatteo & Jean-Franc{c}ois Muzy, 2015. "Hawkes processes in finance," Papers 1502.04592, arXiv.org, revised May 2015.
    2. Emmanuel Bacry & Thibault Jaisson & Jean--François Muzy, 2016. "Estimation of slowly decreasing Hawkes kernels: application to high-frequency order book dynamics," Quantitative Finance, Taylor & Francis Journals, vol. 16(8), pages 1179-1201, August.
    3. Rama Cont & Sasha Stoikov & Rishi Talreja, 2010. "A Stochastic Model for Order Book Dynamics," Operations Research, INFORMS, vol. 58(3), pages 549-563, June.
    4. Eric Smith & J Doyne Farmer & Laszlo Gillemot & Supriya Krishnamurthy, 2003. "Statistical theory of the continuous double auction," Quantitative Finance, Taylor & Francis Journals, vol. 3(6), pages 481-514.
    5. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frederic Abergel, 2011. "Econophysics review: I. Empirical facts," Quantitative Finance, Taylor & Francis Journals, vol. 11(7), pages 991-1012.
    6. Bowsher, Clive G., 2007. "Modelling security market events in continuous time: Intensity based, multivariate point process models," Journal of Econometrics, Elsevier, vol. 141(2), pages 876-912, December.
    7. 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.
    8. Frédéric Abergel & Aymen Jedidi, 2015. "Long-Time Behavior of a Hawkes Process--Based Limit Order Book," Post-Print hal-01121711, HAL.
    9. Abergel,Frédéric & Anane,Marouane & Chakraborti,Anirban & Jedidi,Aymen & Muni Toke,Ioane, 2016. "Limit Order Books," Cambridge Books, Cambridge University Press, number 9781107163980, September.
    10. Large, Jeremy, 2007. "Measuring the resiliency of an electronic limit order book," Journal of Financial Markets, Elsevier, vol. 10(1), pages 1-25, February.
    11. repec:hal:wpaper:hal-01121711 is not listed on IDEAS
    12. Frédéric Abergel & Anirban Chakraborti & Aymen Jedidi & Ioane Muni Toke & Marouane Anane, 2016. "Limit Order Books," Post-Print hal-02177394, HAL.
    13. 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.
    14. Zoltán Eisler & Jean-Philippe Bouchaud & Julien Kockelkoren, 2012. "The price impact of order book events: market orders, limit orders and cancellations," Quantitative Finance, Taylor & Francis Journals, vol. 12(9), pages 1395-1419, September.
    15. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frédéric Abergel, 2011. "Econophysics review: I. Empirical facts," Post-Print hal-00621058, HAL.
    16. Emmanuel Bacry & Sylvain Delattre & Marc Hoffmann & Jean-François Muzy, 2013. "Modelling microstructure noise with mutually exciting point processes," Post-Print hal-01313995, HAL.
    17. Parameswaran Gopikrishnan & Vasiliki Plerou & Xavier Gabaix & H. Eugene Stanley, 2000. "Statistical Properties of Share Volume Traded in Financial Markets," Papers cond-mat/0008113, arXiv.org.
    18. Marcello Rambaldi & Emmanuel Bacry & Fabrizio Lillo, 2016. "The role of volume in order book dynamics: a multivariate Hawkes process analysis," Papers 1602.07663, arXiv.org.
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    Cited by:

    1. Marcello Rambaldi & Emmanuel Bacry & Jean-Franc{c}ois Muzy, 2018. "Disentangling and quantifying market participant volatility contributions," Papers 1807.07036, arXiv.org.
    2. Ana Roldan Contreras & Anatoliy Swishchuk, 2022. "Optimal Liquidation, Acquisition and Market Making Problems in HFT under Hawkes Models for LOB," Risks, MDPI, vol. 10(8), pages 1-32, August.

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