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Price Dynamics in a Markovian Limit Order Market

  • 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)

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    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.

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    File URL: http://hal.archives-ouvertes.fr/docs/00/68/17/62/PDF/ContLarrard2010.pdf
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    Paper provided by HAL in its series Post-Print with number hal-00552252.

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    Date of creation: 03 Jan 2013
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    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
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    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. Engle, Robert F & Lunde, Asger, 1998. "Trades and Quotes: A Bivariate Point Process," University of California at San Diego, Economics Working Paper Series qt8bh079sq, Department of Economics, UC San Diego.
    4. 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.
    5. Eric Smith & J. Doyne Farmer & Laszlo Gillemot & Supriya Krishnamurthy, 2002. "Statistical theory of the continuous double auction," Papers cond-mat/0210475, arXiv.org.
    6. 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.
    7. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    8. Burton Hollifield & Robert A. Miller & Patrik Sandas, 2004. "Empirical Analysis of Limit Order Markets," Review of Economic Studies, Wiley Blackwell, vol. 71(4), pages 1027-1063, October.
    9. 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.
    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. 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.
    12. Parlour, Christine A, 1998. "Price Dynamics in Limit Order Markets," Review of Financial Studies, Society for Financial Studies, vol. 11(4), pages 789-816.
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