IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v127y2017i8p2447-2481.html
   My bibliography  Save this article

A one-level limit order book model with memory and variable spread

Author

Listed:
  • Chávez-Casillas, Jonathan A.
  • Figueroa-López, José E.

Abstract

Motivated by Cont and de Larrard (2013)’s seminal Limit Order Book (LOB) model, we propose a new model for the level I of a LOB in which the arrivals of orders and cancellations are still assumed to be mutually independent, memoryless, and stationary, but, unlike the aforementioned paper, the information about the standing orders at the opposite side of the book after each price change and the arrivals of new orders within the spread are incorporated. Our main result gives a diffusion approximation for the mid-price process, which sheds further light on the relation between the mid-price behavior at low frequencies and some LOB features not considered in earlier works. To illustrate the applicability of the proposed framework, we also develop a feasible method to compute several quantities of interest, such as the distribution of the time span between price changes and the probability of consecutive price increments conditioned on the current state of the book. These LOB model features are relevant in many applications such as high frequency trading and intraday risk management. The proposed method is also used to develop an efficient simulation scheme for the price dynamics, which is then applied to assess numerically the accuracy of the diffusion approximation.

Suggested Citation

  • Chávez-Casillas, Jonathan A. & Figueroa-López, José E., 2017. "A one-level limit order book model with memory and variable spread," Stochastic Processes and their Applications, Elsevier, vol. 127(8), pages 2447-2481.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:8:p:2447-2481
    DOI: 10.1016/j.spa.2016.11.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414916302150
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2016.11.005?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Martin D. Gould & Mason A. Porter & Stacy Williams & Mark McDonald & Daniel J. Fenn & Sam D. Howison, 2013. "Limit order books," Quantitative Finance, Taylor & Francis Journals, vol. 13(11), pages 1709-1742, November.
    2. Eric Smith & J Doyne Farmer & Laszlo Gillemot & Supriya Krishnamurthy, 2003. "Statistical theory of the continuous double auction," Quantitative Finance, Taylor & Francis Journals, vol. 3(6), pages 481-514.
    3. Ioane Muni Toke & Fabrizio Pomponio, 2012. "Modelling Trades-Through in a Limit Order Book Using Hawkes Processes," Post-Print hal-00745554, HAL.
    4. Rama Cont & Adrien De Larrard, 2012. "Order book dynamics in liquid markets: limit theorems and diffusion approximations," Papers 1202.6412, arXiv.org.
    5. Rama Cont & Adrien de Larrard, 2013. "Price Dynamics in a Markovian Limit Order Market," Post-Print hal-00552252, HAL.
    6. Martin D. Gould & Mason A. Porter & Stacy Williams & Mark McDonald & Daniel J. Fenn & Sam D. Howison, 2010. "Limit Order Books," Papers 1012.0349, arXiv.org, revised Apr 2013.
    7. Toke, Ioane Muni & Pomponio, Fabrizio, 2012. "Modelling trades-through in a limit order book using hawkes processes," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 6, pages 1-23.
    8. Rama Cont & Sasha Stoikov & Rishi Talreja, 2010. "A Stochastic Model for Order Book Dynamics," Operations Research, INFORMS, vol. 58(3), pages 549-563, June.
    9. Hugh Luckock, 2003. "A steady-state model of the continuous double auction," Quantitative Finance, Taylor & Francis Journals, vol. 3(5), pages 385-404.
    10. Jean-Philippe Bouchaud & J. Doyne Farmer & Fabrizio Lillo, 2008. "How markets slowly digest changes in supply and demand," Papers 0809.0822, arXiv.org.
    11. Ioanid Rosu, 2009. "A Dynamic Model of the Limit Order Book," Post-Print hal-00515873, HAL.
    12. 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.
    13. Łukasz Kruk, 2003. "Functional Limit Theorems for a Simple Auction," Mathematics of Operations Research, INFORMS, vol. 28(4), pages 716-751, November.
    14. Ioanid Rosu, 2009. "A Dynamic Model of the Limit Order Book," Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4601-4641, November.
    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)

    Citations

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


    Cited by:

    1. 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.
    2. Rama Cont & Marvin Muller, 2019. "A Stochastic Pde Model For Limit Order Book Dynamics," Working Papers hal-02090449, HAL.
    3. Matthew F Dixon, 2017. "A High Frequency Trade Execution Model for Supervised Learning," Papers 1710.03870, arXiv.org, revised Dec 2017.
    4. Justin Sirignano & Rama Cont, 2018. "Universal features of price formation in financial markets: perspectives from Deep Learning," Papers 1803.06917, arXiv.org.
    5. Justin Sirignano & Rama Cont, 2018. "Universal features of price formation in financial markets: perspectives from Deep Learning," Working Papers hal-01754054, HAL.
    6. Matthew F Dixon, 2017. "Sequence Classification of the Limit Order Book using Recurrent Neural Networks," Papers 1707.05642, 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. 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.
    2. 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.
    3. Ulrich Horst & Michael Paulsen, 2015. "A law of large numbers for limit order books," Papers 1501.00843, arXiv.org.
    4. M. Derksen & B. Kleijn & R. de Vilder, 2019. "Clearing price distributions in call auctions," Papers 1904.07583, arXiv.org, revised Nov 2019.
    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. Weibing Huang & Mathieu Rosenbaum & Pamela Saliba, 2019. "From Glosten-Milgrom to the whole limit order book and applications to financial regulation," Papers 1902.10743, arXiv.org.
    7. 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.
    8. Marcello Rambaldi & Emmanuel Bacry & Jean-Franc{c}ois Muzy, 2018. "Disentangling and quantifying market participant volatility contributions," Papers 1807.07036, arXiv.org.
    9. Kyungsub Lee & Byoung Ki Seo, 2021. "Analytic formula for option margin with liquidity costs under dynamic delta hedging," Papers 2103.15302, arXiv.org.
    10. Ben Hambly & Jasdeep Kalsi & James Newbury, 2018. "Limit order books, diffusion approximations and reflected SPDEs: from microscopic to macroscopic models," Papers 1808.07107, arXiv.org, revised Jun 2019.
    11. Nicolas Baradel & Bruno Bouchard & David Evangelista & Othmane Mounjid, 2019. "Optimal inventory management and order book modeling," Post-Print hal-01710301, HAL.
    12. 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.
    13. 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.
    14. Johannes Bleher & Michael Bleher & Thomas Dimpfl, 2020. "From orders to prices: A stochastic description of the limit order book to forecast intraday returns," Papers 2004.11953, arXiv.org, revised May 2021.
    15. Weibing Huang & Charles-Albert Lehalle & Mathieu Rosenbaum, 2015. "Simulating and Analyzing Order Book Data: The Queue-Reactive Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 107-122, March.
    16. Rama Cont & Pierre Degond & Xuan Lifan, 2023. "A mathematical framework for modelling order book dynamics," Working Papers hal-03968767, HAL.
    17. Alexander Lykov & Stepan Muzychka & Kirill Vaninsky, 2016. "Investor'S Sentiment In Multi-Agent Model Of The Continuous Double Auction," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(06), pages 1-29, September.
    18. Rama Cont & Pierre Degond & Lifan Xuan, 2023. "A mathematical framework for modelling order book dynamics," Papers 2302.01169, arXiv.org.
    19. Aymen Jedidi & Frédéric Abergel, 2013. "Stability and price scaling limit of a Hawkes-process based order book model," Working Papers hal-00821607, HAL.
    20. Ioane Muni Toke, 2015. "Stationary distribution of the volume at the best quote in a Poisson order book model," Papers 1502.03871, arXiv.org.

    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:eee:spapps:v:127:y:2017:i:8:p:2447-2481. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.