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Non-parametric Estimation of Quadratic Hawkes Processes for Order Book Events

Author

Listed:
  • Antoine Fosset
  • Jean-Philippe Bouchaud
  • Michael Benzaquen

    (LadHyX - Laboratoire d'hydrodynamique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique)

Abstract

We propose an actionable calibration procedure for general Quadratic Hawkes models of order book events (market orders, limit orders, cancellations). One of the main features of such models is to encode not only the influence of past events on future events but also, crucially, the influence of past price changes on such events. We show that the empirically calibrated quadratic kernel is well described by a diagonal contribution (that captures past realised volatility), plus a rank-one "Zumbach" contribution (that captures the effect of past trends). We find that the Zumbach kernel is a power-law of time, as are all other feedback kernels. As in many previous studies, the rate of truly exogenous events is found to be a small fraction of the total event rate. These two features suggest that the system is close to a critical point -- in the sense that stronger feedback kernels would lead to instabilities.

Suggested Citation

  • Antoine Fosset & Jean-Philippe Bouchaud & Michael Benzaquen, 2021. "Non-parametric Estimation of Quadratic Hawkes Processes for Order Book Events," Post-Print hal-02998555, HAL.
    • Handle: RePEc:hal:journl:hal-02998555
    Note: View the original document on HAL open archive server: https://hal.science/hal-02998555
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    References listed on IDEAS

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