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Multivariate General Compound Point Processes in Limit Order Books

Author

Listed:
  • Qi Guo

    (Department of Mathematics and Statistics, University of Calgary, 2500 University Drive NW, Calgary, AB T2N 1N4, Canada)

  • Bruno Remillard

    (Department of Decision Sciences, HEC Montréal, 3000 Chemin de la Cote-Sainte-Catherine, Montréal, QC H3T 2A7, Canada)

  • Anatoliy Swishchuk

    (Department of Mathematics and Statistics, University of Calgary, 2500 University Drive NW, Calgary, AB T2N 1N4, Canada)

Abstract

In this paper, we focus on a new generalization of multivariate general compound Hawkes process (MGCHP), which we referred to as the multivariate general compound point process (MGCPP). Namely, we applied a multivariate point process to model the order flow instead of the Hawkes process. The law of large numbers (LLN) and two functional central limit theorems (FCLTs) for the MGCPP were proved in this work. Applications of the MGCPP in the limit order market were also considered. We provided numerical simulations and comparisons for the MGCPP and MGCHP by applying Google, Apple, Microsoft, Amazon, and Intel trading data.

Suggested Citation

  • Qi Guo & Bruno Remillard & Anatoliy Swishchuk, 2020. "Multivariate General Compound Point Processes in Limit Order Books," Risks, MDPI, vol. 8(3), pages 1-20, September.
    • Handle: RePEc:gam:jrisks:v:8:y:2020:i:3:p:98-:d:412414
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    References listed on IDEAS

    as
    1. Anatoliy Swishchuk & Aiden Huffman, 2020. "General Compound Hawkes Processes in Limit Order Books," Risks, MDPI, vol. 8(1), pages 1-25, March.
    2. Bergmeir, Christoph & Hyndman, Rob J. & Koo, Bonsoo, 2018. "A note on the validity of cross-validation for evaluating autoregressive time series prediction," Computational Statistics & Data Analysis, Elsevier, vol. 120(C), pages 70-83.
    3. Ban Zheng & François Roueff & Frédéric Abergel, 2014. "Ergodicity and scaling limit of a constrained multivariate Hawkes process," Post-Print hal-00777941, HAL.
    4. Bacry, E. & Delattre, S. & Hoffmann, M. & Muzy, J.F., 2013. "Some limit theorems for Hawkes processes and application to financial statistics," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2475-2499.
    5. Bowsher, Clive G., 2007. "Modelling security market events in continuous time: Intensity based, multivariate point process models," Journal of Econometrics, Elsevier, vol. 141(2), pages 876-912, December.
    6. Anatoliy Swishchuk & Tyler Hofmeister & Katharina Cera & Julia Schmidt, 2017. "General Semi-Markov Model For Limit Order Books," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(03), pages 1-21, May.
    7. Rama Cont & Adrien de Larrard, 2013. "Price Dynamics in a Markovian Limit Order Market," Post-Print hal-00552252, HAL.
    8. Luc, BAUWENS & Nikolaus, HAUTSCH, 2006. "Modelling Financial High Frequency Data Using Point Processes," Discussion Papers (ECON - Département des Sciences Economiques) 2006039, Université catholique de Louvain, Département des Sciences Economiques.
    9. Ban Zheng & Franc{c}ois Roueff & Fr'ed'eric Abergel, 2013. "Ergodicity and scaling limit of a constrained multivariate Hawkes process," Papers 1301.5007, arXiv.org, revised Feb 2014.
    10. Anatoliy Swishchuk, 2017. "Risk Model Based on General Compound Hawkes Process," Papers 1706.09038, arXiv.org.
    11. B. Prakasa Rao, 2009. "Conditional independence, conditional mixing and conditional association," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(2), pages 441-460, June.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Luca Lalor & Anatoliy Swishchuk, 2024. "Reinforcement Learning in Non-Markov Market-Making," Papers 2410.14504, arXiv.org, revised Nov 2024.
    2. Qi Guo & Anatoliy Swishchuk & Bruno R'emillard, 2022. "Multivariate Hawkes-based Models in LOB: European, Spread and Basket Option Pricing," Papers 2209.07621, arXiv.org.
    3. 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.
    4. Myles Sjogren & Timothy DeLise, 2021. "General Compound Hawkes Processes for Mid-Price Prediction," Papers 2110.07075, arXiv.org.

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