IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1608.01795.html
   My bibliography  Save this paper

A diffusion approximation for limit order book models

Author

Listed:
  • Ulrich Horst
  • Dorte Kreher

Abstract

This paper derives a diffusion approximation for a sequence of discrete-time one-sided limit order book models with non-linear state dependent order arrival and cancellation dynamics. The discrete time sequences are specified in terms of an $\R_+$-valued best bid price process and an $L^2_{loc}$-valued volume process. It is shown that under suitable assumptions the sequence of interpolated discrete time models is relatively compact in a localized sense and that any limit point satisfies a certain infinite dimensional SDE. Under additional assumptions on the dependence structure we construct two classes of models, which fit in the general framework, such that the limiting SDE admits a unique solution and thus the discrete dynamics converge to a diffusion limit in a localized sense.

Suggested Citation

  • Ulrich Horst & Dorte Kreher, 2016. "A diffusion approximation for limit order book models," Papers 1608.01795, arXiv.org, revised Aug 2017.
    • Handle: RePEc:arx:papers:1608.01795
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1608.01795
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Cho, Nhansook, 1995. "Weak convergence of stochastic integrals driven by martingale measure," Stochastic Processes and their Applications, Elsevier, vol. 59(1), pages 55-79, September.
    2. Rama Cont & Adrien de Larrard, 2013. "Price Dynamics in a Markovian Limit Order Market," Post-Print hal-00552252, HAL.
    3. Ulrich Horst & Dorte Kreher, 2015. "A weak law of large numbers for a limit order book model with fully state dependent order dynamics," Papers 1502.04359, arXiv.org, revised May 2016.
    4. Christian Bayer & Ulrich Horst & Jinniao Qiu, 2014. "A Functional Limit Theorem for Limit Order Books with State Dependent Price Dynamics," Papers 1405.5230, arXiv.org, revised Aug 2016.
    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. 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.

    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. 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.
    2. Xin Guo & Zhao Ruan & Lingjiong Zhu, 2015. "Dynamics of Order Positions and Related Queues in a Limit Order Book," Papers 1505.04810, arXiv.org, revised Oct 2015.
    3. Weibing Huang & Mathieu Rosenbaum, 2015. "Ergodicity and diffusivity of Markovian order book models: a general framework," Papers 1505.04936, arXiv.org.
    4. Ulrich Horst & Dorte Kreher, 2015. "A weak law of large numbers for a limit order book model with fully state dependent order dynamics," Papers 1502.04359, arXiv.org, revised May 2016.
    5. 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.
    6. Philippe Bergault & Olivier Gu'eant, 2023. "Liquidity Dynamics in RFQ Markets and Impact on Pricing," Papers 2309.04216, arXiv.org, revised Jun 2024.
    7. Antonio Briola & Silvia Bartolucci & Tomaso Aste, 2024. "Deep Limit Order Book Forecasting," Papers 2403.09267, arXiv.org, revised Jun 2024.
    8. Jonathan A. Chávez Casillas, 2024. "A Time-Dependent Markovian Model of a Limit Order Book," Computational Economics, Springer;Society for Computational Economics, vol. 63(2), pages 679-709, February.
    9. 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.
    10. Anatoliy Swishchuk & Nelson Vadori, 2016. "A Semi-Markovian Modeling of Limit Order Markets," Papers 1601.01710, arXiv.org.
    11. Philippe Bergault & Enzo Cogn'eville, 2024. "Simulating and analyzing a sparse order book: an application to intraday electricity markets," Papers 2410.06839, arXiv.org.
    12. 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).
    13. Alessandro Micheli & Johannes Muhle‐Karbe & Eyal Neuman, 2023. "Closed‐loop Nash competition for liquidity," Mathematical Finance, Wiley Blackwell, vol. 33(4), pages 1082-1118, October.
    14. Jonathan A. Ch'avez-Casillas & Jos'e E. Figueroa-L'opez, 2014. "One-level limit order book models with memory and variable spread," Papers 1407.5684, arXiv.org, revised Mar 2016.
    15. Weibing Huang & Sergio Pulido & Mathieu Rosenbaum & Pamela Saliba & Emmanouil Sfendourakis, 2019. "From Glosten-Milgrom to the whole limit order book and applications to financial regulation," Papers 1902.10743, arXiv.org, revised Mar 2025.
    16. Ulrich Horst & Dörte Kreher, 2018. "Second order approximations for limit order books," Finance and Stochastics, Springer, vol. 22(4), pages 827-877, October.
    17. Gao, Xuefeng & Xu, Tianrun, 2022. "Order scoring, bandit learning and order cancellations," Journal of Economic Dynamics and Control, Elsevier, vol. 134(C).
    18. Robert J. Elliott & Dilip B. Madan & Tak Kuen Siu, 2021. "Two price economic equilibria and financial market bid/ask prices," Annals of Finance, Springer, vol. 17(1), pages 27-43, March.
    19. Matthew F Dixon, 2017. "Sequence Classification of the Limit Order Book using Recurrent Neural Networks," Papers 1707.05642, arXiv.org.
    20. Rama Cont & Marvin S. Mueller, 2019. "A stochastic partial differential equation model for limit order book dynamics," Papers 1904.03058, arXiv.org, revised May 2021.

    More about this item

    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:1608.01795. 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.