IDEAS home Printed from https://ideas.repec.org/a/taf/quantf/v3y2003i5p385-404.html
   My bibliography  Save this article

A steady-state model of the continuous double auction

Author

Listed:
  • Hugh Luckock

Abstract

A model of the continuous double auction is constructed and analysed. Given the underlying supply and demand functions, the analysis yields steady-state probability distributions for the best ask, best bid and transaction prices. Under fairly general assumptions it is found that these prices are confined to a clearly defined window. Expressions are also obtained for the depth of the order book at arbitrary prices, and for the expected time-to-execution of a given order. These can be used to calculate the optimal order price for a trader with a specified level of impatience, to determine when a market order is preferable to a limit order, and hence in some cases to detect the presence of irrational or ill-informed traders in the market. It is conjectured that, in a market of rational and well-informed traders, the two sides of the order book should be statistically independent.

Suggested Citation

  • Hugh Luckock, 2003. "A steady-state model of the continuous double auction," Quantitative Finance, Taylor & Francis Journals, vol. 3(5), pages 385-404.
  • Handle: RePEc:taf:quantf:v:3:y:2003:i:5:p:385-404
    DOI: 10.1088/1469-7688/3/5/305
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1088/1469-7688/3/5/305
    Download Restriction: Access to full text is restricted to subscribers.

    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. 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.
    2. Bollerslev, Tim & Domowitz, Ian & Wang, Jianxin, 1997. "Order flow and the bid-ask spread: An empirical probability model of screen-based trading," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1471-1491, June.
    3. Vernon L. Smith, 1962. "An Experimental Study of Competitive Market Behavior," Journal of Political Economy, University of Chicago Press, vol. 70, pages 322-322.
    4. Carl Chiarella & Giulia Iori, 2002. "A simulation analysis of the microstructure of double auction markets," Quantitative Finance, Taylor & Francis Journals, vol. 2(5), pages 346-353.
    5. Glosten, Lawrence R, 1994. " Is the Electronic Open Limit Order Book Inevitable?," Journal of Finance, American Finance Association, vol. 49(4), pages 1127-1161, September.
    6. Chakravarty Sugato & Holden Craig W., 1995. "An Integrated Model of Market and Limit Orders," Journal of Financial Intermediation, Elsevier, vol. 4(3), pages 213-241, July.
    7. Mendelson, Haim, 1982. "Market Behavior in a Clearing House," Econometrica, Econometric Society, vol. 50(6), pages 1505-1524, November.
    8. Maslov, Sergei, 2000. "Simple model of a limit order-driven market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 278(3), pages 571-578.
    9. Marc Potters & Jean-Philippe Bouchaud, 2002. "More statistical properties of order books and price impact," Science & Finance (CFM) working paper archive 0210710, Science & Finance, Capital Fund Management.
    10. Domowitz, Ian & Wang, Jianxin, 1994. "Auctions as algorithms : Computerized trade execution and price discovery," Journal of Economic Dynamics and Control, Elsevier, vol. 18(1), pages 29-60, 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. Zoltan Eisler & Janos Kertesz & Fabrizio Lillo & Rosario Mantegna, 2009. "Diffusive behavior and the modeling of characteristic times in limit order executions," Quantitative Finance, Taylor & Francis Journals, vol. 9(5), pages 547-563.
    2. Sandrine Jacob Leal & Mauro Napoletano & Andrea Roventini & Giorgio Fagiolo, 2016. "Rock around the clock: An agent-based model of low- and high-frequency trading," Journal of Evolutionary Economics, Springer, vol. 26(1), pages 49-76, March.
    3. repec:eee:spapps:v:127:y:2017:i:8:p:2447-2481 is not listed on IDEAS
    4. Anatoliy Swishchuk & Nelson Vadori, 2016. "A Semi-Markovian Modeling of Limit Order Markets," Papers 1601.01710, arXiv.org.
    5. Sandrine Jacob Leal & Mauro Napoletano & Andrea Roventini & Giorgio Fagiolo, 2016. "Rock around the clock: An agent-based model of low- and high-frequency trading," Journal of Evolutionary Economics, Springer, vol. 26(1), pages 49-76, March.
    6. Enrico Scalas & Rudolf Gorenflo & Hugh Luckock & Francesco Mainardi & Maurizio Mantelli & Marco Raberto, 2004. "Anomalous waiting times in high-frequency financial data," Quantitative Finance, Taylor & Francis Journals, vol. 4(6), pages 695-702.
    7. Chiarella, Carl & Iori, Giulia, 2009. "The impact of heterogeneous trading rules on the limit order book and order flows," Journal of Economic Dynamics and Control, Elsevier, vol. 33(3), pages 525-537.
    8. Kühn, Christoph & Stroh, Maximilian, 2013. "Continuous time trading of a small investor in a limit order market," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 2011-2053.
    9. Enrico Scalas, 2005. "Five Years of Continuous-time Random Walks in Econophysics," Papers cond-mat/0501261, arXiv.org.
    10. Matthieu Wyart & Jean-Philippe Bouchaud & Julien Kockelkoren & Marc Potters & Michele Vettorazzo, 2006. "Relation between Bid-Ask Spread, Impact and Volatility in Double Auction Markets," Science & Finance (CFM) working paper archive 500067, Science & Finance, Capital Fund Management.
    11. Erhan Bayraktar & Ulrich Horst & Ronnie Sircar, 2007. "Queueing Theoretic Approaches to Financial Price Fluctuations," Papers math/0703832, arXiv.org.
    12. 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.
    13. V'it Perv{z}ina & Jan M. Swart, 2016. "How many market makers does a market need?," Papers 1612.00981, arXiv.org.
    14. Kuroda, Koji & Murai, Joshin, 2007. "Limit theorems in financial market models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(1), pages 28-34.
    15. Scalas, Enrico, 2006. "The application of continuous-time random walks in finance and economics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 362(2), pages 225-239.
    16. Krause, Andreas, 2006. "Fat tails and multi-scaling in a simple model of limit order markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 368(1), pages 183-190.
    17. Khalil Dayri & Mathieu Rosenbaum, 2012. "Large tick assets: implicit spread and optimal tick size," Papers 1207.6325, arXiv.org, revised Jan 2013.

    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:taf:quantf:v:3:y:2003:i:5:p:385-404. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Chris Longhurst). General contact details of provider: http://www.tandfonline.com/RQUF20 .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.