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Non-parametric estimation of quadratic Hawkes processes for order book events

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  • Antoine Fosset
  • Jean-Philippe Bouchaud
  • Michael Benzaquen

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 slightly stronger feedback kernels would lead to endogenous liquidity crises.

Suggested Citation

  • Antoine Fosset & Jean-Philippe Bouchaud & Michael Benzaquen, 2022. "Non-parametric estimation of quadratic Hawkes processes for order book events," The European Journal of Finance, Taylor & Francis Journals, vol. 28(7), pages 663-678, May.
    • Handle: RePEc:taf:eurjfi:v:28:y:2022:i:7:p:663-678
    DOI: 10.1080/1351847X.2021.1917441
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    Cited by:

    1. Timoth'ee Fabre & Ioane Muni Toke, 2024. "Neural Hawkes: Non-Parametric Estimation in High Dimension and Causality Analysis in Cryptocurrency Markets," Papers 2401.09361, arXiv.org, revised Jan 2024.

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