IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2008.00124.html
   My bibliography  Save this paper

Multivariate General Compound Point Processes in Limit Order Books

Author

Listed:
  • Qi Guo
  • Bruno Remillard
  • Anatoliy Swishchuk

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. 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," Papers 2008.00124, arXiv.org.
    • Handle: RePEc:arx:papers:2008.00124
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2008.00124
    File Function: Latest version
    Download Restriction: no
    ---><---

    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. 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.
    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. Tata Subba Rao & Granville Tunnicliffe Wilson & Michael Eichler & Rainer Dahlhaus & Johannes Dueck, 2017. "Graphical Modeling for Multivariate Hawkes Processes with Nonparametric Link Functions," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(2), pages 225-242, March.
    7. BAUWENS, Luc & HAUTSCH, Nikolaus, 2006. "Modelling financial high frequency data using point processes," LIDAM Discussion Papers CORE 2006080, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. 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.
    9. 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.
    10. Jonathan A. Ch'avez-Casillas & Robert J. Elliott & Bruno R'emillard & Anatoliy V. Swishchuk, 2017. "A level-1 Limit Order book with time dependent arrival rates," Papers 1704.06572, arXiv.org.
    11. Marcello Rambaldi & Emmanuel Bacry & Fabrizio Lillo, 2017. "The role of volume in order book dynamics: a multivariate Hawkes process analysis," Quantitative Finance, Taylor & Francis Journals, vol. 17(7), pages 999-1020, July.
    12. Anatoliy Swishchuk, 2017. "Risk Model Based on General Compound Hawkes Process," Papers 1706.09038, arXiv.org.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. Myles Sjogren & Timothy DeLise, 2021. "General Compound Hawkes Processes for Mid-Price Prediction," Papers 2110.07075, arXiv.org.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. Anatoliy Swishchuk & Aiden Huffman, 2018. "General Compound Hawkes Processes in Limit Order Books," Papers 1812.02298, arXiv.org.
    3. Anatoliy Swishchuk, 2021. "Modelling of Limit Order Books by General Compound Hawkes Processes with Implementations," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 399-428, March.
    4. Anatoliy Swishchuk & Bruno Remillard & Robert Elliott & Jonathan Chavez-Casillas, 2017. "Compound Hawkes Processes in Limit Order Books," Papers 1712.03106, arXiv.org.
    5. Anatoliy Swishchuk, 2017. "General Compound Hawkes Processes in Limit Order Books," Papers 1706.07459, arXiv.org, revised Jun 2017.
    6. Emmanuel Bacry & Iacopo Mastromatteo & Jean-Franc{c}ois Muzy, 2015. "Hawkes processes in finance," Papers 1502.04592, arXiv.org, revised May 2015.
    7. Anatoliy Swishchuk & Aiden Huffman, 2020. "General Compound Hawkes Processes in Limit Order Books," Risks, MDPI, vol. 8(1), pages 1-25, March.
    8. 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.
    9. 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.
    10. Roueff, Francois & von Sachs, Rainer & Sansonnet, Laure, 2015. "Time-frequency analysis of locally stationary Hawkes processes," LIDAM Discussion Papers ISBA 2015011, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    11. Fan, Lina & Yang, Hao & Zhai, Jia & Zhang, Xiaotao, 2023. "Forecasting stock volatility during the stock market crash period: The role of Hawkes process," Finance Research Letters, Elsevier, vol. 55(PA).
    12. Jiwook Jang & Rosy Oh, 2020. "A Bivariate Compound Dynamic Contagion Process for Cyber Insurance," Papers 2007.04758, arXiv.org.
    13. 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.
    14. Anatoliy Swishchuk, 2021. "Merton Investment Problems in Finance and Insurance for the Hawkes-Based Models," Risks, MDPI, vol. 9(6), pages 1-13, June.
    15. Kyungsub Lee, 2022. "Application of Hawkes volatility in the observation of filtered high-frequency price process in tick structures," Papers 2207.05939, arXiv.org, revised Sep 2024.
    16. Huang, Lorick & Khabou, Mahmoud, 2023. "Nonlinear Poisson autoregression and nonlinear Hawkes processes," Stochastic Processes and their Applications, Elsevier, vol. 161(C), pages 201-241.
    17. Ioane Muni Toke & Nakahiro Yoshida, 2020. "Marked point processes and intensity ratios for limit order book modeling," Papers 2001.08442, arXiv.org.
    18. Ban Zheng & François Roueff & Frédéric Abergel, 2014. "Ergodicity and scaling limit of a constrained multivariate Hawkes process," Post-Print hal-00777941, HAL.
    19. Steffen Volkenand & Günther Filler & Martin Odening, 2020. "Price Discovery and Market Reflexivity in Agricultural Futures Contracts with Different Maturities," Risks, MDPI, vol. 8(3), pages 1-17, July.
    20. Massil Achab & Emmanuel Bacry & Jean-Franc{c}ois Muzy & Marcello Rambaldi, 2017. "Analysis of order book flows using a nonparametric estimation of the branching ratio matrix," Papers 1706.03411, arXiv.org.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2008.00124. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.