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General Compound Hawkes Processes in Limit Order Books

Author

Listed:
  • Anatoliy Swishchuk

    (Department of Mathematics and Statistics, Faculty of Science, Calgary, AL T2N1N4, Canada
    These authors contributed equally to this work.)

  • Aiden Huffman

    (Department of Mathematics and Statistics, Faculty of Science, Calgary, AL T2N1N4, Canada
    These authors contributed equally to this work.)

Abstract

In this paper, we study various new Hawkes processes. Specifically, we construct general compound Hawkes processes and investigate their properties in limit order books. With regard to these general compound Hawkes processes, we prove a Law of Large Numbers (LLN) and a Functional Central Limit Theorems (FCLT) for several specific variations. We apply several of these FCLTs to limit order books to study the link between price volatility and order flow, where the volatility in mid-price changes is expressed in terms of parameters describing the arrival rates and mid-price process.

Suggested Citation

  • Anatoliy Swishchuk & Aiden Huffman, 2020. "General Compound Hawkes Processes in Limit Order Books," Risks, MDPI, vol. 8(1), pages 1-25, March.
    • Handle: RePEc:gam:jrisks:v:8:y:2020:i:1:p:28-:d:332592
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. Chiranjit Dutta & Kara Karpman & Sumanta Basu & Nalini Ravishanker, 2023. "Review of Statistical Approaches for Modeling High-Frequency Trading Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 1-48, May.
    3. Huang, Lorick & Khabou, Mahmoud, 2023. "Nonlinear Poisson autoregression and nonlinear Hawkes processes," Stochastic Processes and their Applications, Elsevier, vol. 161(C), pages 201-241.
    4. 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.
    5. Myles Sjogren & Timothy DeLise, 2021. "General Compound Hawkes Processes for Mid-Price Prediction," Papers 2110.07075, arXiv.org.
    6. Zhicheng Li & Haipeng Xing, 2022. "High-Frequency Quote Volatility Measurement Using a Change-Point Intensity Model," Mathematics, MDPI, vol. 10(4), pages 1-24, February.
    7. Luca Lalor & Anatoliy Swishchuk, 2024. "Algorithmic and High-Frequency Trading Problems for Semi-Markov and Hawkes Jump-Diffusion Models," Papers 2409.12776, arXiv.org.
    8. Souhail Chebbi & Senda Ounaies, 2023. "Optimal Investment of Merton Model for Multiple Investors with Frictions," Mathematics, MDPI, vol. 11(13), pages 1-10, June.
    9. Anatoliy Swishchuk, 2021. "Merton Investment Problems in Finance and Insurance for the Hawkes-based Models," Papers 2104.02694, arXiv.org, revised May 2021.
    10. Anatoliy Swishchuk, 2021. "Merton Investment Problems in Finance and Insurance for the Hawkes-Based Models," Risks, MDPI, vol. 9(6), pages 1-13, June.
    11. Qi Guo & Bruno Remillard & Anatoliy Swishchuk, 2020. "Multivariate General Compound Point Processes in Limit Order Books," Papers 2008.00124, arXiv.org.

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