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Analysis of order book flows using a non-parametric estimation of the branching ratio matrix

Author

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  • M. Achab
  • E. Bacry
  • J. F. Muzy
  • M. Rambaldi

Abstract

We introduce a new non-parametric method that allows for a direct, fast and efficient estimation of the matrix of kernel norms of a multivariate Hawkes process, also called branching ratio matrix. We demonstrate the capabilities of this method by applying it to high-frequency order book data from the EUREX exchange. We show that it is able to uncover (or recover) various relationships between all the first-level order book events associated with some asset when mapped to a 12-dimensional process. We then scale up the model so as to account for events on two assets simultaneously and we discuss the joint high-frequency dynamics.

Suggested Citation

  • M. Achab & E. Bacry & J. F. Muzy & M. Rambaldi, 2018. "Analysis of order book flows using a non-parametric estimation of the branching ratio matrix," Quantitative Finance, Taylor & Francis Journals, vol. 18(2), pages 199-212, February.
    • Handle: RePEc:taf:quantf:v:18:y:2018:i:2:p:199-212
    DOI: 10.1080/14697688.2017.1403132
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    Citations

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    Cited by:

    1. Maxime Morariu-Patrichi & Mikko S. Pakkanen, 2018. "State-dependent Hawkes processes and their application to limit order book modelling," Papers 1809.08060, arXiv.org, revised Sep 2021.
    2. Antoine Fosset & Jean-Philippe Bouchaud & Michael Benzaquen, 2020. "Non-parametric Estimation of Quadratic Hawkes Processes for Order Book Events," Working Papers hal-02998555, HAL.
    3. Antoine Fosset & Jean-Philippe Bouchaud & Michael Benzaquen, 2020. "Endogenous Liquidity Crises," Post-Print hal-02567495, HAL.
    4. Antoine Fosset & Jean-Philippe Bouchaud & Michael Benzaquen, 2021. "Non-parametric Estimation of Quadratic Hawkes Processes for Order Book Events," Post-Print hal-02998555, HAL.
    5. Antoine Fosset & Jean-Philippe Bouchaud & Michael Benzaquen, 2020. "Endogenous Liquidity Crises," Working Papers hal-02567495, HAL.
    6. Antoine Fosset & Jean-Philippe Bouchaud & Michael Benzaquen, 2019. "Endogenous Liquidity Crises," Papers 1912.00359, arXiv.org, revised Feb 2020.
    7. Maxime Morariu-Patrichi & Mikko Pakkanen, 2018. "State-dependent Hawkes processes and their application to limit order book modelling," CREATES Research Papers 2018-26, Department of Economics and Business Economics, Aarhus University.
    8. Antoine Fosset & Jean-Philippe Bouchaud & Michael Benzaquen, 2020. "Non-parametric Estimation of Quadratic Hawkes Processes for Order Book Events," Papers 2005.05730, arXiv.org.
    9. Privault, Nicolas, 2021. "Recursive computation of the Hawkes cumulants," Statistics & Probability Letters, Elsevier, vol. 177(C).

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