IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2609.36631.html

A Spread-Gated Hawkes-Flocking Model for Best Bid and Ask Dynamics, with an Application to Limit Order Placement

Author

Listed:
  • Hyoeun Lee
  • Kiseop Lee

Abstract

We study the joint dynamics of the best bid and ask prices with a spread-gated Hawkes-flocking model. The model tracks four types of best-quote movements: spread-narrowing movements are switched off when the spread is at its one-tick minimum, and a cross-side excitation term, whose activation depends on the prevailing spread, links the two sides of the book. We show that the process is non-explosive on every finite horizon, give an $O(N)$ recursive likelihood, and validate the maximum likelihood estimator by simulation. On real intraday limit order book data for two large-tick stocks, INTC and MSFT, the restriction that removes the cross-side term is rejected, and the full model improves fit substantially by AIC and BIC; the likelihood is multimodal on a single day, so estimation uses a multi-start search. As an application, we derive the closed-form optimal size of a single-period limit order placed at the best or second-best quote, given the model's next-event probabilities and externally supplied execution probabilities.

Suggested Citation

  • Hyoeun Lee & Kiseop Lee, 2026. "A Spread-Gated Hawkes-Flocking Model for Best Bid and Ask Dynamics, with an Application to Limit Order Placement," Papers 2609.36631, arXiv.org.
    • Handle: RePEc:arx:papers:2609.36631
    as

    Download full text from publisher

    File URL: https://arxiv.org/pdf/2609.36631
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Aurélien Alfonsi & Pierre Blanc, 2016. "Dynamic optimal execution in a mixed-market-impact Hawkes price model," Finance and Stochastics, Springer, vol. 20(1), pages 183-218, January.
    2. M. Achab & E. Bacry & J. F. Muzy & M. Rambaldi, 2018. "Analysis of order book flows using a non-parametric estimation of the branching ratio matrix," Quantitative Finance, Taylor & Francis Journals, vol. 18(2), pages 199-212, February.
    3. Hyun Jin Jang & Kiseop Lee & Kyungsub Lee, 2020. "Systemic risk in market microstructure of crude oil and gasoline futures prices: A Hawkes flocking model approach," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(2), pages 247-275, February.
    4. Choi, So Eun & Jang, Hyun Jin & Lee, Kyungsub & Zheng, Harry, 2021. "Optimal market-Making strategies under synchronised order arrivals with deep neural networks," Journal of Economic Dynamics and Control, Elsevier, vol. 125(C).
    5. 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.
    6. Emmanuel Bacry & Iacopo Mastromatteo & Jean-Franc{c}ois Muzy, 2015. "Hawkes processes in finance," Papers 1502.04592, arXiv.org, revised May 2015.
    7. repec:hal:wpaper:hal-01121711 is not listed on IDEAS
    8. Matthias Kirchner, 2017. "An estimation procedure for the Hawkes process," Quantitative Finance, Taylor & Francis Journals, vol. 17(4), pages 571-595, April.
    9. Aurélien Alfonsi & Pierre Blanc, 2016. "Dynamic optimal execution in a mixed-market-impact Hawkes price model," Finance and Stochastics, Springer, vol. 20(1), pages 183-218, January.
    10. Maxime Morariu-Patrichi & Mikko S. Pakkanen, 2022. "State-dependent Hawkes processes and their application to limit order book modelling," Quantitative Finance, Taylor & Francis Journals, vol. 22(3), pages 563-583, March.
    11. Jain, Konark & Firoozye, Nick & Kochems, Jonathan & Treleaven, Philip, 2024. "Limit Order Book dynamics and order size modelling using Compound Hawkes Process," Finance Research Letters, Elsevier, vol. 69(PA).
    12. Aurélien Alfonsi & Pierre Blanc, 2016. "Dynamic optimal execution in a mixed-market-impact Hawkes price model," Post-Print hal-00971369, HAL.
    13. Kyungsub Lee, 2026. "Forecasting duration in high-frequency financial data using a self-exciting flexible residual point process," Papers 2604.00346, arXiv.org, revised Aug 2026.
    14. E. Bacry & S. Delattre & M. Hoffmann & J. F. Muzy, 2013. "Modelling microstructure noise with mutually exciting point processes," Quantitative Finance, Taylor & Francis Journals, vol. 13(1), pages 65-77, January.
    15. Frédéric Abergel & Aymen Jedidi, 2015. "Long-Time Behavior of a Hawkes Process--Based Limit Order Book," Post-Print hal-01121711, HAL.
    16. Emmanuel Bacry & Sylvain Delattre & Marc Hoffmann & Jean-François Muzy, 2013. "Modelling microstructure noise with mutually exciting point processes," Post-Print hal-01313995, HAL.
    17. Kyungsub Lee & Byoung Ki Seo, 2023. "Modeling Bid and Ask Price Dynamics with an Extended Hawkes Process and Its Empirical Applications for High-Frequency Stock Market Data," Journal of Financial Econometrics, Oxford University Press, vol. 21(4), pages 1099-1142.
    Full references (including those not matched with items on IDEAS)

    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. Antoine Fosset & Jean-Philippe Bouchaud & Michael Benzaquen, 2020. "Non-parametric Estimation of Quadratic Hawkes Processes for Order Book Events," Papers 2005.05730, arXiv.org.
    2. Antoine Fosset & Jean-Philippe Bouchaud & Michael Benzaquen, 2020. "Non-parametric Estimation of Quadratic Hawkes Processes for Order Book Events," Working Papers hal-02998555, HAL.
    3. Antoine Fosset & Jean-Philippe Bouchaud & Michael Benzaquen, 2021. "Non-parametric Estimation of Quadratic Hawkes Processes for Order Book Events," Post-Print hal-02998555, HAL.
    4. Maxime Morariu-Patrichi & Mikko S. Pakkanen, 2017. "Hybrid marked point processes: characterisation, existence and uniqueness," Papers 1707.06970, arXiv.org, revised Oct 2018.
    5. Guanxing Fu & Ulrich Horst & Xiaonyu Xia, 2020. "Portfolio Liquidation Games with Self-Exciting Order Flow," Papers 2011.05589, arXiv.org.
    6. José Da Fonseca & Riadh Zaatour, 2017. "Correlation and Lead–Lag Relationships in a Hawkes Microstructure Model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 37(3), pages 260-285, March.
    7. Fu, Guanxing & Horst, Ulrich & Xia, Xiaonyu, 2022. "Portfolio Liquidation Games with Self-Exciting Order Flow," Rationality and Competition Discussion Paper Series 327, CRC TRR 190 Rationality and Competition.
    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. 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.
    11. Da Fonseca, José & Malevergne, Yannick, 2021. "A simple microstructure model based on the Cox-BESQ process with application to optimal execution policy," Journal of Economic Dynamics and Control, Elsevier, vol. 128(C).
    12. Jain, Konark & Firoozye, Nick & Kochems, Jonathan & Treleaven, Philip, 2024. "Limit Order Book dynamics and order size modelling using Compound Hawkes Process," Finance Research Letters, Elsevier, vol. 69(PA).
    13. Sadoghi, Amirhossein & Vecer, Jan, 2022. "Optimal liquidation problem in illiquid markets," European Journal of Operational Research, Elsevier, vol. 296(3), pages 1050-1066.
    14. Amirhossein Sadoghi & Jan Vecer, 2022. "Optimal liquidation problem in illiquid markets," Post-Print hal-03696768, HAL.
    15. Dupret, Jean-Loup & Hainaut, Donatien, 2023. "Optimal liquidation under indirect price impact with propagator," LIDAM Discussion Papers ISBA 2023012, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    16. Ingemar Kaj & Mine Caglar, 2017. "A buffer Hawkes process for limit order books," Papers 1710.03506, arXiv.org.
    17. Ying Chen & Ulrich Horst & Hoang Hai Tran, 2026. "Optimal Trade Execution Under Endogenous Order Flow," Operations Research, INFORMS, vol. 74(1), pages 72-92, January.
    18. Xiaofei Lu & Frédéric Abergel, 2017. "Limit order book modelling with high dimensional Hawkes processes," Working Papers hal-01512430, HAL.
    19. Clinet, Simon & Yoshida, Nakahiro, 2017. "Statistical inference for ergodic point processes and application to Limit Order Book," Stochastic Processes and their Applications, Elsevier, vol. 127(6), pages 1800-1839.
    20. Ziyi Wang & Carmine Ventre & Maria Polukarov, 2025. "ARL-Based Multi-Action Market Making with Hawkes Processes and Variable Volatility," Papers 2508.16589, 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:2609.36631. 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: https://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.