IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v485y2017icp61-72.html
   My bibliography  Save this article

Low-traffic limit and first-passage times for a simple model of the continuous double auction

Author

Listed:
  • Scalas, Enrico
  • Rapallo, Fabio
  • Radivojević, Tijana

Abstract

We consider a simplified model of the continuous double auction where prices are integers varying from 1 to N with limit orders and market orders, but quantity per order limited to a single share. For this model, the order process is equivalent to two M∕M∕1 queues. We study the behavior of the auction in the low-traffic limit where limit orders are immediately matched by market orders. In this limit, the distribution of prices can be computed exactly and gives a reasonable approximation of the price distribution when the ratio between the rate of order arrivals and the rate of order executions is below 1∕2. This is further confirmed by the analysis of the first-passage time in 1 or N.

Suggested Citation

  • Scalas, Enrico & Rapallo, Fabio & Radivojević, Tijana, 2017. "Low-traffic limit and first-passage times for a simple model of the continuous double auction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 485(C), pages 61-72.
  • Handle: RePEc:eee:phsmap:v:485:y:2017:i:c:p:61-72
    DOI: 10.1016/j.physa.2017.05.020
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437117305319
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

    File URL: https://libkey.io/10.1016/j.physa.2017.05.020?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Tijana Radivojević & Jonatha Anselmi & Enrico Scalas, 2012. "A stylized model for the continuous double auction," Lecture Notes in Economics and Mathematical Systems, in: Andrea Teglio & Simone Alfarano & Eva Camacho-Cuena & Miguel Ginés-Vilar (ed.), Managing Market Complexity, edition 127, chapter 0, pages 115-125, Springer.
    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. B. Tóth & E. Scalas & J. Huber & M. Kirchler, 2007. "The value of information in a multi-agent market model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 55(1), pages 115-120, January.
    4. Scalas, Enrico & Kaizoji, Taisei & Kirchler, Michael & Huber, Jürgen & Tedeschi, Alessandra, 2006. "Waiting times between orders and trades in double-auction markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 463-471.
    5. Rama Cont & Adrien De Larrard, 2012. "Order book dynamics in liquid markets: limit theorems and diffusion approximations," Papers 1202.6412, arXiv.org.
    6. Rama Cont & Adrien de Larrard, 2013. "Price Dynamics in a Markovian Limit Order Market," Post-Print hal-00552252, HAL.
    7. Gode, Dhananjay K & Sunder, Shyam, 1993. "Allocative Efficiency of Markets with Zero-Intelligence Traders: Market as a Partial Substitute for Individual Rationality," Journal of Political Economy, University of Chicago Press, vol. 101(1), pages 119-137, February.
    8. Jose Blanchet & Xinyun Chen, 2013. "Continuous-time Modeling of Bid-Ask Spread and Price Dynamics in Limit Order Books," Papers 1310.1103, arXiv.org.
    9. Marco Raberto & Fabio Rapallo & Enrico Scalas, 2011. "Semi-Markov Graph Dynamics," PLOS ONE, Public Library of Science, vol. 6(8), pages 1-13, August.
    10. Bondesson, Lennart, 1991. "A characterization of first passage time distributions for random walks," Stochastic Processes and their Applications, Elsevier, vol. 39(1), pages 81-88, October.
    11. Bottazzi, Giulio & Dosi, Giovanni & Rebesco, Igor, 2005. "Institutional architectures and behavioral ecologies in the dynamics of financial markets," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 197-228, February.
    12. Tijana Radivojević & Jonatha Anselmi & Enrico Scalas, 2014. "Ergodic Transition in a Simple Model of the Continuous Double Auction," PLOS ONE, Public Library of Science, vol. 9(2), pages 1-5, February.
    13. Anufriev, Mikhail & Panchenko, Valentyn, 2009. "Asset prices, traders' behavior and market design," Journal of Economic Dynamics and Control, Elsevier, vol. 33(5), pages 1073-1090, May.
    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. Zhang, Yunyi & Gong, Pu, 2018. "IPV model with Cobb–Douglas and reference-dependent utility functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 121-131.
    2. V'it Perv{z}ina & Jan M. Swart, 2016. "How much market making does a market need?," Papers 1612.00981, arXiv.org, revised Jun 2018.

    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. Tijana Radivojević & Jonatha Anselmi & Enrico Scalas, 2014. "Ergodic Transition in a Simple Model of the Continuous Double Auction," PLOS ONE, Public Library of Science, vol. 9(2), pages 1-5, February.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Chia-Hsuan Yeh & Chun-Yi Yang, 2013. "Do price limits hurt the market?," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 8(1), pages 125-153, April.
    7. Nicolas Baradel & Bruno Bouchard & David Evangelista & Othmane Mounjid, 2019. "Optimal inventory management and order book modeling," Post-Print hal-01710301, HAL.
    8. Rama Cont & Marvin Muller, 2019. "A Stochastic Pde Model For Limit Order Book Dynamics," Working Papers hal-02090449, HAL.
    9. Schinckus, C., 2013. "Between complexity of modelling and modelling of complexity: An essay on econophysics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3654-3665.
    10. 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.
    11. Michiel Leur & Mikhail Anufriev, 2018. "Timing under individual evolutionary learning in a continuous double auction," Journal of Evolutionary Economics, Springer, vol. 28(3), pages 609-631, August.
    12. Nicolas Baradel & Bruno Bouchard & David Evangelista & Othmane Mounjid, 2018. "Optimal inventory management and order book modeling," Working Papers hal-01710301, HAL.
    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. Nicolas Baradel & Bruno Bouchard & David Evangelista & Othmane Mounjid, 2018. "Optimal inventory management and order book modeling," Papers 1802.08135, arXiv.org, revised Nov 2018.
    15. Robin Nicole & Aleksandra Alori'c & Peter Sollich, 2020. "Fragmentation in trader preferences among multiple markets: Market coexistence versus single market dominance," Papers 2012.04103, arXiv.org, revised Aug 2021.
    16. 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.
    17. A. O. Glekin & A. Lykov & K. L. Vaninsky, 2014. "On Simulation of Various Effects in Consolidated Order Book," Papers 1402.4150, arXiv.org.
    18. Anatoliy Swishchuk & Nelson Vadori, 2016. "A Semi-Markovian Modeling of Limit Order Markets," Papers 1601.01710, arXiv.org.
    19. Thibault Jaisson, 2015. "Liquidity and Impact in Fair Markets," Papers 1506.02507, arXiv.org.
    20. 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.

    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:phsmap:v:485:y:2017:i:c:p:61-72. 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.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.