IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1405.5230.html
   My bibliography  Save this paper

A Functional Limit Theorem for Limit Order Books with State Dependent Price Dynamics

Author

Listed:
  • Christian Bayer
  • Ulrich Horst
  • Jinniao Qiu

Abstract

We consider a stochastic model for the dynamics of the two-sided limit order book (LOB). Our model is flexible enough to allow for a dependence of the price dynamics on volumes. For the joint dynamics of best bid and ask prices and the standing buy and sell volume densities, we derive a functional limit theorem, which states that our LOB model converges in distribution to a fully coupled SDE-SPDE system when the order arrival rates tend to infinity and the impact of an individual order arrival on the book as well as the tick size tends to zero. The SDE describes the bid/ask price dynamics while the SPDE describes the volume dynamics.

Suggested Citation

  • 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.
    • Handle: RePEc:arx:papers:1405.5230
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1405.5230
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Horst, Ulrich & Rothe, Christian, 2008. "Queuing, Social Interactions, And The Microstructure Of Financial Markets," Macroeconomic Dynamics, Cambridge University Press, vol. 12(2), pages 211-233, April.
    2. Glosten, Lawrence R. & Milgrom, Paul R., 1985. "Bid, ask and transaction prices in a specialist market with heterogeneously informed traders," Journal of Financial Economics, Elsevier, vol. 14(1), pages 71-100, March.
    3. Rama Cont & Adrien De Larrard, 2012. "Order book dynamics in liquid markets: limit theorems and diffusion approximations," Papers 1202.6412, arXiv.org.
    4. Rama Cont & Adrien de Larrard, 2013. "Price Dynamics in a Markovian Limit Order Market," Post-Print hal-00552252, HAL.
    5. Easley, David & O'Hara, Maureen, 1987. "Price, trade size, and information in securities markets," Journal of Financial Economics, Elsevier, vol. 19(1), pages 69-90, September.
    6. Darrell Duffie & Philip Protter, 1992. "From Discrete‐ to Continuous‐Time Finance: Weak Convergence of the Financial Gain Process1," Mathematical Finance, Wiley Blackwell, vol. 2(1), pages 1-15, January.
    7. Rama Cont & Sasha Stoikov & Rishi Talreja, 2010. "A Stochastic Model for Order Book Dynamics," Operations Research, INFORMS, vol. 58(3), pages 549-563, June.
    8. 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.
    9. Ioanid Rosu, 2009. "A Dynamic Model of the Limit Order Book," Post-Print hal-00515873, HAL.
    10. Erhan Bayraktar & Ulrich Horst & Ronnie Sircar, 2007. "Queueing Theoretic Approaches to Financial Price Fluctuations," Papers math/0703832, arXiv.org.
    11. Łukasz Kruk, 2003. "Functional Limit Theorems for a Simple Auction," Mathematics of Operations Research, INFORMS, vol. 28(4), pages 716-751, November.
    12. Hans Föllmer & Martin Schweizer, 1993. "A Microeconomic Approach to Diffusion Models For Stock Prices," Mathematical Finance, Wiley Blackwell, vol. 3(1), pages 1-23, January.
    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 & Dorte Kreher, 2017. "Second order approximations for limit order books," Papers 1708.07394, arXiv.org, revised Mar 2018.
    2. Ulrich Horst & Dorte Kreher, 2016. "A diffusion approximation for limit order book models," Papers 1608.01795, arXiv.org, revised Aug 2017.
    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.

    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 & Michael Paulsen, 2017. "A Law of Large Numbers for Limit Order Books," Mathematics of Operations Research, INFORMS, vol. 42(4), pages 1280-1312, November.
    2. Ulrich Horst & Michael Paulsen, 2015. "A law of large numbers for limit order books," Papers 1501.00843, arXiv.org.
    3. Sadoghi, Amirhossein & Vecer, Jan, 2022. "Optimal liquidation problem in illiquid markets," European Journal of Operational Research, Elsevier, vol. 296(3), pages 1050-1066.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Dimitri Vayanos & Jiang Wang, 2012. "Market Liquidity -- Theory and Empirical Evidence," NBER Working Papers 18251, National Bureau of Economic Research, Inc.
    10. 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.
    11. Vayanos, Dimitri & Wang, Jiang, 2013. "Market Liquidity—Theory and Empirical Evidence ," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 1289-1361, Elsevier.
    12. Roberto Pascual & David Veredas, 2010. "Does the Open Limit Order Book Matter in Explaining Informational Volatility?," Journal of Financial Econometrics, Oxford University Press, vol. 8(1), pages 57-87, Winter.
    13. René Carmona & Kevin Webster, 2019. "The self-financing equation in limit order book markets," Finance and Stochastics, Springer, vol. 23(3), pages 729-759, July.
    14. Amirhossein Sadoghi & Jan Vecer, 2022. "Optimal liquidation problem in illiquid markets," Post-Print hal-03696768, HAL.
    15. Nikolsko-Rzhevska, Olena & Nikolsko-Rzhevskyy, Alex & Black, Jeffrey R., 2020. "The life of U’s: Order revisions on NASDAQ," Journal of Banking & Finance, Elsevier, vol. 111(C).
    16. Baron Law & Frederi Viens, 2019. "Market Making under a Weakly Consistent Limit Order Book Model," Papers 1903.07222, arXiv.org, revised Jan 2020.
    17. 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.
    18. Alessio Emanuele Biondo, 2020. "Information versus imitation in a real-time agent-based model of financial markets," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 15(3), pages 613-631, July.
    19. M. Derksen & B. Kleijn & R. de Vilder, 2019. "Clearing price distributions in call auctions," Papers 1904.07583, arXiv.org, revised Nov 2019.
    20. 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.

    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:1405.5230. 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.