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Limit Order Book Dynamics and Order Size Modelling Using Compound Hawkes Process

Author

Listed:
  • Konark Jain
  • Nick Firoozye
  • Jonathan Kochems
  • Philip Treleaven

Abstract

Hawkes Process has been used to model Limit Order Book (LOB) dynamics in several ways in the literature however the focus has been limited to capturing the inter-event times while the order size is usually assumed to be constant. We propose a novel methodology of using Compound Hawkes Process for the LOB where each event has an order size sampled from a calibrated distribution. The process is formulated in a novel way such that the spread of the process always remains positive. Further, we condition the model parameters on time of day to support empirical observations. We make use of an enhanced non-parametric method to calibrate the Hawkes kernels and allow for inhibitory cross-excitation kernels. We showcase the results and quality of fits for an equity stock's LOB in the NASDAQ exchange and compare them against several baselines. Finally, we conduct a market impact study of the simulator and show the empirical observation of a concave market impact function is indeed replicated.

Suggested Citation

  • Konark Jain & Nick Firoozye & Jonathan Kochems & Philip Treleaven, 2023. "Limit Order Book Dynamics and Order Size Modelling Using Compound Hawkes Process," Papers 2312.08927, arXiv.org, revised Mar 2024.
    • Handle: RePEc:arx:papers:2312.08927
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    References listed on IDEAS

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    1. Kyungsub Lee & Byoung Ki Seo, 2022. "Modeling bid and ask price dynamics with an extended Hawkes process and its empirical applications for high-frequency stock market data," Papers 2201.10173, arXiv.org.
    2. Matthias Kirchner, 2017. "An estimation procedure for the Hawkes process," Quantitative Finance, Taylor & Francis Journals, vol. 17(4), pages 571-595, April.
    3. Emmanuel Bacry & Thibault Jaisson & Jean--François Muzy, 2016. "Estimation of slowly decreasing Hawkes kernels: application to high-frequency order book dynamics," Quantitative Finance, Taylor & Francis Journals, vol. 16(8), pages 1179-1201, August.
    4. Matthias Kirchner & Silvan Vetter, 2022. "Hawkes model specification for limit order books," The European Journal of Finance, Taylor & Francis Journals, vol. 28(7), pages 642-662, May.
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