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Hawkes model for price and trades high-frequency dynamics

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  • E. Bacry
  • J. F Muzy

Abstract

We introduce a multivariate Hawkes process that accounts for the dynamics of market prices through the impact of market order arrivals at microstructural level. Our model is a point process mainly characterized by 4 kernels associated with respectively the trade arrival self-excitation, the price changes mean reversion the impact of trade arrivals on price variations and the feedback of price changes on trading activity. It allows one to account for both stylized facts of market prices microstructure (including random time arrival of price moves, discrete price grid, high frequency mean reversion, correlation functions behavior at various time scales) and the stylized facts of market impact (mainly the concave-square-root-like/relaxation characteristic shape of the market impact of a meta-order). Moreover, it allows one to estimate the entire market impact profile from anonymous market data. We show that these kernels can be estimated from the empirical conditional mean intensities. We provide numerical examples, application to real data and comparisons to former approaches.

Suggested Citation

  • E. Bacry & J. F Muzy, 2013. "Hawkes model for price and trades high-frequency dynamics," Papers 1301.1135, arXiv.org.
    • Handle: RePEc:arx:papers:1301.1135
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    References listed on IDEAS

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    1. 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.
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    5. 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.
    6. Emmanuel Bacry & Sylvain Delattre & Marc Hoffmann & Jean-François Muzy, 2013. "Modelling microstructure noise with mutually exciting point processes," Post-Print hal-01313995, HAL.
    7. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
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    Citations

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    Cited by:

    1. Emmanuel Bacry & Adrian Iuga & Matthieu Lasnier & Charles-Albert Lehalle, 2014. "Market impacts and the life cycle of investors orders," Papers 1412.0217, arXiv.org, revised Dec 2014.
    2. Damian Eduardo Taranto & Giacomo Bormetti & Fabrizio Lillo, 2014. "The adaptive nature of liquidity taking in limit order books," Papers 1403.0842, arXiv.org, revised Apr 2014.
    3. Thibault Jaisson & Mathieu Rosenbaum, 2013. "Limit theorems for nearly unstable Hawkes processes," Papers 1310.2033, arXiv.org, revised Mar 2015.
    4. Emmanuel Bacry & Jean-Francois Muzy, 2014. "Second order statistics characterization of Hawkes processes and non-parametric estimation," Papers 1401.0903, arXiv.org, revised Feb 2015.
    5. Thibault Jaisson, 2014. "Market impact as anticipation of the order flow imbalance," Papers 1402.1288, arXiv.org.
    6. Bibinger, Markus & Jirak, Moritz & Reiss, Markus, 2014. "Improved volatility estimation based on limit order books," SFB 649 Discussion Papers 2014-053, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    7. Jonathan Sadighian, 2019. "Deep Reinforcement Learning in Cryptocurrency Market Making," Papers 1911.08647, arXiv.org.
    8. Alexander Lipton & Umberto Pesavento & Michael G Sotiropoulos, 2013. "Trade arrival dynamics and quote imbalance in a limit order book," Papers 1312.0514, arXiv.org.
    9. Aur'elien Alfonsi & Pierre Blanc, 2014. "Dynamic optimal execution in a mixed-market-impact Hawkes price model," Papers 1404.0648, arXiv.org, revised Jun 2015.
    10. Aymen Jedidi & Frédéric Abergel, 2013. "Stability and price scaling limit of a Hawkes-process based order book model," Working Papers hal-00821607, HAL.
    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. Jonathan Sadighian, 2020. "Extending Deep Reinforcement Learning Frameworks in Cryptocurrency Market Making," Papers 2004.06985, arXiv.org.
    13. repec:hum:wpaper:sfb649dp2014-053 is not listed on IDEAS
    14. Aurélien Alfonsi & Pierre Blanc, 2016. "Dynamic optimal execution in a mixed-market-impact Hawkes price model," Post-Print hal-00971369, HAL.

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