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High-dimensional Hawkes processes for limit order books: modelling, empirical analysis and numerical calibration

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  • Xiaofei Lu
  • Frédéric Abergel

Abstract

High-dimensional Hawkes processes with exponential kernels are used to describe limit order books in order-driven financial markets. The dependencies between orders of various types are carefully studied and modelled, based on a thorough empirical analysis. The observation of inhibition effects is particularly interesting, and leads us to the use of non-linear Hawkes processes. Specific attention is devoted to the calibration problem, in order to account for the high dimensionality of the problem and the very poor convexity properties of the MLE. Our analyses show a good agreement between the statistical properties of order book data and those of the model.

Suggested Citation

  • Xiaofei Lu & Frédéric Abergel, 2018. "High-dimensional Hawkes processes for limit order books: modelling, empirical analysis and numerical calibration," Quantitative Finance, Taylor & Francis Journals, vol. 18(2), pages 249-264, February.
    • Handle: RePEc:taf:quantf:v:18:y:2018:i:2:p:249-264
    DOI: 10.1080/14697688.2017.1403142
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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. Kramer, Anke & Kiesel, Rüdiger, 2021. "Exogenous factors for order arrivals on the intraday electricity market," Energy Economics, Elsevier, vol. 97(C).
    3. Kanamura, Takashi & Bunn, Derek W., 2022. "Market making and electricity price formation in Japan," Energy Economics, Elsevier, vol. 107(C).
    4. Bruno Gav{s}perov & Zvonko Kostanjv{c}ar, 2022. "Deep Reinforcement Learning for Market Making Under a Hawkes Process-Based Limit Order Book Model," Papers 2207.09951, arXiv.org.
    5. Ioane Muni Toke & Nakahiro Yoshida, 2020. "Marked point processes and intensity ratios for limit order book modeling," Papers 2001.08442, arXiv.org.
    6. Ioane Muni Toke & Nakahiro Yoshida, 2022. "Marked point processes and intensity ratios for limit order book modeling," Post-Print hal-02465428, HAL.
    7. Bilodeau, Yann, 2020. "Deep limit order book events dynamics," Working Papers 20-4, HEC Montreal, Canada Research Chair in Risk Management.
    8. Ana Roldan Contreras & Anatoliy Swishchuk, 2022. "Optimal Liquidation, Acquisition and Market Making Problems in HFT under Hawkes Models for LOB," Risks, MDPI, vol. 10(8), pages 1-32, August.
    9. Hai-Chuan Xu & Wei-Xing Zhou, 2020. "Modeling aggressive market order placements with Hawkes factor models," PLOS ONE, Public Library of Science, vol. 15(1), pages 1-12, January.
    10. 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.
    11. Shunya Chomei, 2023. "Empirical analysis in limit order book modeling for Nikkei 225 Stocks with Cox-type intensities," Papers 2302.01668, arXiv.org, revised Feb 2023.
    12. Emmanouil Sfendourakis & Ioane Muni Toke, 2021. "LOB modeling using Hawkes processes with a state-dependent factor," Papers 2107.12872, arXiv.org, revised Dec 2021.
    13. Jiwook Jang & Rosy Oh, 2020. "A Bivariate Compound Dynamic Contagion Process for Cyber Insurance," Papers 2007.04758, arXiv.org.
    14. 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.
    15. Kyungsub Lee, 2024. "Discrete Hawkes process with flexible residual distribution and filtered historical simulation," Papers 2401.13890, arXiv.org.

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