Advanced Search
MyIDEAS: Login

Price Dynamics in a Markovian Limit Order Market

Contents:

Author Info

  • Rama Cont

    ()
    (LPMA - Laboratoire de Probabilités et Modèles Aléatoires - CNRS : UMR7599 - Université Paris VI - Pierre et Marie Curie - Université Paris VII - Paris Diderot)

  • Adrien De Larrard

    ()
    (LPMA - Laboratoire de Probabilités et Modèles Aléatoires - CNRS : UMR7599 - Université Paris VI - Pierre et Marie Curie - Université Paris VII - Paris Diderot)

Registered author(s):

    Abstract

    We propose and study a simple stochastic model for the dynamics of a limit order book, in which arrivals of market order, limit orders and order cancellations are described in terms of a Markovian queueing system. Through its analytical tractability, the model allows to obtain analytical expressions for various quantities of interest such as the distribution of the duration between price changes, the distribution and autocorrelation of price changes, and the probability of an upward move in the price, conditional on the state of the order book. We study the diffusion limit of the price process and express the volatility of price changes in terms of parameters describing the arrival rates of buy and sell orders and cancelations. These analytical results provide some insight into the relation between order flow and price dynamics in order-driven markets.

    Download Info

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
    File URL: http://hal.archives-ouvertes.fr/docs/00/68/17/62/PDF/ContLarrard2010.pdf
    Download Restriction: no

    Bibliographic Info

    Paper provided by HAL in its series Post-Print with number hal-00552252.

    as in new window
    Length:
    Date of creation: 03 Jan 2013
    Date of revision:
    Publication status: Published, SIAM Journal on Financial Mathematics, 2013, 4, 1, 1-25
    Handle: RePEc:hal:journl:hal-00552252

    Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00552252
    Contact details of provider:
    Web page: http://hal.archives-ouvertes.fr/

    Related research

    Keywords: limit order book; market microstructure; queueing; diffusion limit; high-frequency data; liquidity; duration analysis; point process;

    This paper has been announced in the following NEP Reports:

    References

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
    as in new window
    1. Aurelien Alfonsi & Antje Fruth & Alexander Schied, 2010. "Optimal execution strategies in limit order books with general shape functions," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 143-157.
    2. Gourieroux, Christian & Jasiak, Joanna & Le Fol, Gaelle, 1999. "Intra-day market activity," Journal of Financial Markets, Elsevier, vol. 2(3), pages 193-226, August.
    3. Robert F. Engle & Asger Lunde, 2003. "Trades and Quotes: A Bivariate Point Process," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 1(2), pages 159-188.
    4. Burton Hollifield & Robert A. Miller & Patrik Sand�s, 2004. "Empirical Analysis of Limit Order Markets," Review of Economic Studies, Oxford University Press, vol. 71(4), pages 1027-1063.
    5. Burton Hollifield & Robert Miller & Patrik Sandas, . "Empirical Analysis of Limit Order Markets," GSIA Working Papers -290183991, Carnegie Mellon University, Tepper School of Business.
    6. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    7. 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.
    8. Christian Y. Robert & Mathieu Rosenbaum, 2011. "A New Approach for the Dynamics of Ultra-High-Frequency Data: The Model with Uncertainty Zones," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 9(2), pages 344-366, Spring.
    9. Parlour, Christine A, 1998. "Price Dynamics in Limit Order Markets," Review of Financial Studies, Society for Financial Studies, vol. 11(4), pages 789-816.
    10. Harris, Lawrence E. & Panchapagesan, Venkatesh, 2005. "The information content of the limit order book: evidence from NYSE specialist trading decisions," Journal of Financial Markets, Elsevier, vol. 8(1), pages 25-67, February.
    11. Eric Smith & J. Doyne Farmer & Laszlo Gillemot & Supriya Krishnamurthy, 2002. "Statistical theory of the continuous double auction," Papers cond-mat/0210475, arXiv.org.
    12. Aur\'elien Alfonsi & Antje Fruth & Alexander Schied, 2007. "Optimal execution strategies in limit order books with general shape functions," Papers 0708.1756, arXiv.org, revised Feb 2010.
    13. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
    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 in new window

    Cited by:
    1. Qinghua Li, 2014. "Facilitation and Internalization Optimal Strategy in a Multilateral Trading Context," Papers 1404.7320, arXiv.org.
    2. Weibing Huang & Charles-Albert Lehalle & Mathieu Rosenbaum, 2013. "Simulating and analyzing order book data: The queue-reactive model," Papers 1312.0563, arXiv.org.
    3. Rene Carmona & Kevin Webster, 2013. "The Self-Financing Equation in High Frequency Markets," Papers 1312.2302, arXiv.org.
    4. Christian Bayer & Ulrich Horst & Jinniao Qiu, 2014. "A Functional Limit Theorem for Limit Order Books," Papers 1405.5230, arXiv.org.
    5. Aur\'elien Alfonsi & Pierre Blanc, 2014. "Dynamic optimal execution in a mixed-market-impact Hawkes price model," Papers 1404.0648, arXiv.org.
    6. Jose Blanchet & Xinyun Chen, 2013. "Continuous-time Modeling of Bid-Ask Spread and Price Dynamics in Limit Order Books," Papers 1310.1103, arXiv.org.
    7. Aurélien Alfonsi & Pierre Blanc, 2014. "Dynamic optimal execution in a mixed-market-impact Hawkes price model," Working Papers hal-00971369, HAL.
    8. Hans F\"ollmer & Alexander Schied, 2013. "Probabilistic aspects of finance," Papers 1309.7759, arXiv.org.

    Lists

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    Statistics

    Access and download statistics

    Corrections

    When requesting a correction, please mention this item's handle: RePEc:hal:journl:hal-00552252. 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: (CCSD).

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 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.