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Estimation of slowly decreasing Hawkes kernels: Application to high frequency order book modelling

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  • Emmanuel Bacry
  • Thibault Jaisson
  • Jean-Francois Muzy

Abstract

We present a modified version of the non parametric Hawkes kernel estimation procedure studied in arXiv:1401.0903 that is adapted to slowly decreasing kernels. We show on numerical simulations involving a reasonable number of events that this method allows us to estimate faithfully a power-law decreasing kernel over at least 6 decades. We then propose a 8-dimensional Hawkes model for all events associated with the first level of some asset order book. Applying our estimation procedure to this model, allows us to uncover the main properties of the coupled dynamics of trade, limit and cancel orders in relationship with the mid-price variations.

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  • Emmanuel Bacry & Thibault Jaisson & Jean-Francois Muzy, 2014. "Estimation of slowly decreasing Hawkes kernels: Application to high frequency order book modelling," Papers 1412.7096, arXiv.org.
    • Handle: RePEc:arx:papers:1412.7096
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    References listed on IDEAS

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    Cited by:

    1. Clinet, Simon & Yoshida, Nakahiro, 2017. "Statistical inference for ergodic point processes and application to Limit Order Book," Stochastic Processes and their Applications, Elsevier, vol. 127(6), pages 1800-1839.
    2. Matthias Kirchner, 2017. "An estimation procedure for the Hawkes process," Quantitative Finance, Taylor & Francis Journals, vol. 17(4), pages 571-595, April.
    3. Thibault Jaisson, 2015. "Liquidity and Impact in Fair Markets," Papers 1506.02507, arXiv.org.
    4. Thibault Jaisson & Mathieu Rosenbaum, 2015. "Rough fractional diffusions as scaling limits of nearly unstable heavy tailed Hawkes processes," Papers 1504.03100, arXiv.org.

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