IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1709.01292.html
   My bibliography  Save this paper

A Scaling Limit for Limit Order Books Driven by Hawkes Processes

Author

Listed:
  • Ulrich Horst
  • Wei Xu

Abstract

In this paper we derive a scaling limit for an infinite dimensional limit order book model driven by Hawkes random measures. The dynamics of the incoming order flow is allowed to depend on the current market price as well as on a volume indicator. With our choice of scaling the dynamics converges to a coupled SDE-ODE system where limiting best bid and ask price processes follows a diffusion dynamics, the limiting volume density functions follows an ODE in a Hilbert space and the limiting order arrival and cancellation intensities follow a Volterra-Fredholm integral equation.

Suggested Citation

  • Ulrich Horst & Wei Xu, 2017. "A Scaling Limit for Limit Order Books Driven by Hawkes Processes," Papers 1709.01292, arXiv.org, revised Aug 2018.
    • Handle: RePEc:arx:papers:1709.01292
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1709.01292
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Emmanuel Bacry & Iacopo Mastromatteo & Jean-Franc{c}ois Muzy, 2015. "Hawkes processes in finance," Papers 1502.04592, arXiv.org, revised May 2015.
    2. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frederic Abergel, 2011. "Econophysics review: II. Agent-based models," Quantitative Finance, Taylor & Francis Journals, vol. 11(7), pages 1013-1041.
    3. Biais, Bruno & Hillion, Pierre & Spatt, Chester, 1995. "An Empirical Analysis of the Limit Order Book and the Order Flow in the Paris Bourse," Journal of Finance, American Finance Association, vol. 50(5), pages 1655-1689, December.
    4. Frédéric Abergel & Aymen Jedidi, 2013. "A Mathematical Approach To Order Book Modeling," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(05), pages 1-40.
    5. Xuefeng Gao & S. J. Deng, 2014. "Hydrodynamic limit of order book dynamics," Papers 1411.7502, arXiv.org, revised Feb 2016.
    6. Thibault Jaisson & Mathieu Rosenbaum, 2013. "Limit theorems for nearly unstable Hawkes processes," Papers 1310.2033, arXiv.org, revised Mar 2015.
    7. Frédéric Abergel & Aymen Jedidi, 2015. "Long-Time Behavior of a Hawkes Process--Based Limit Order Book," Post-Print hal-01121711, HAL.
    8. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frédéric Abergel, 2011. "Econophysics review: II. Agent-based models," Post-Print hal-00621059, HAL.
    9. 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.
    10. Erhan Bayraktar & Ulrich Horst & Ronnie Sircar, 2007. "Queueing Theoretic Approaches to Financial Price Fluctuations," Papers math/0703832, arXiv.org.
    11. repec:hal:wpaper:hal-01121711 is not listed on IDEAS
    12. Emmanuel Bacry & Jean-Fran�ois Muzy, 2014. "Hawkes model for price and trades high-frequency dynamics," Quantitative Finance, Taylor & Francis Journals, vol. 14(7), pages 1147-1166, July.
    13. Rama Cont & Adrien de Larrard, 2013. "Price Dynamics in a Markovian Limit Order Market," Post-Print hal-00552252, HAL.
    14. Cebiroğlu, Gökhan & Horst, Ulrich, 2015. "Optimal order display in limit order markets with liquidity competition," Journal of Economic Dynamics and Control, Elsevier, vol. 58(C), pages 81-100.
    15. Frédéric Abergel & Aymen Jedidi, 2013. "A Mathematical Approach to Order Book Modelling," Post-Print hal-00621253, HAL.
    16. Frederic Abergel & Aymen Jedidi, 2010. "A Mathematical Approach to Order Book Modeling," Papers 1010.5136, arXiv.org, revised Mar 2013.
    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. Ulrich Horst & Dörte Kreher, 2018. "Second order approximations for limit order books," Finance and Stochastics, Springer, vol. 22(4), pages 827-877, October.
    2. Ulrich Horst & Michael Paulsen, 2017. "A Law of Large Numbers for Limit Order Books," Mathematics of Operations Research, INFORMS, vol. 42(4), pages 1280-1312, November.
    3. 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.
    4. Ulrich Horst & Michael Paulsen, 2015. "A law of large numbers for limit order books," Papers 1501.00843, arXiv.org.
    5. Simon Clinet, 2020. "Quasi-likelihood analysis for marked point processes and application to marked Hawkes processes," Papers 2001.11624, arXiv.org, revised Aug 2021.
    6. Aleksejus Kononovicius & Julius Ruseckas, 2018. "Order book model with herd behavior exhibiting long-range memory," Papers 1809.02772, arXiv.org, revised Apr 2019.
    7. Kononovicius, Aleksejus & Ruseckas, Julius, 2019. "Order book model with herd behavior exhibiting long-range memory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 171-191.
    8. 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.
    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. Marcello Rambaldi & Emmanuel Bacry & Jean-Franc{c}ois Muzy, 2018. "Disentangling and quantifying market participant volatility contributions," Papers 1807.07036, arXiv.org.
    11. Lee, Kyungsub & Seo, Byoung Ki, 2017. "Marked Hawkes process modeling of price dynamics and volatility estimation," Journal of Empirical Finance, Elsevier, vol. 40(C), pages 174-200.
    12. Hua, Jia-Chen & Chen, Lijian & Falcon, Liberty & McCauley, Joseph L. & Gunaratne, Gemunu H., 2015. "Variable diffusion in stock market fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 221-233.
    13. Mohammad Zare & Omid Naghshineh Arjmand & Erfan Salavati & Adel Mohammadpour, 2021. "An Agent‐Based model for Limit Order Book: Estimation and simulation," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(1), pages 1112-1121, January.
    14. Kyungsub Lee & Byoung Ki Seo, 2021. "Analytic formula for option margin with liquidity costs under dynamic delta hedging," Papers 2103.15302, arXiv.org.
    15. 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.
    16. Simon Clinet, 2022. "Quasi-likelihood analysis for marked point processes and application to marked Hawkes processes," Statistical Inference for Stochastic Processes, Springer, vol. 25(2), pages 189-225, July.
    17. Xin Liu & Qi Gong & Vidyadhar G. Kulkarni, 2015. "A Stochastic Model of Order Book Dynamics using Bouncing Geometric Brownian Motions," Papers 1511.04096, arXiv.org, revised Mar 2016.
    18. 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).
    19. Ioane Muni Toke, 2017. "Stationary Distribution Of The Volume At The Best Quote In A Poisson Order Book Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(06), pages 1-22, September.
    20. M. Derksen & B. Kleijn & R. de Vilder, 2019. "Clearing price distributions in call auctions," Papers 1904.07583, arXiv.org, revised Nov 2019.

    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:1709.01292. 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.