Price Dynamics in a Markovian Limit Order Market
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.
|Date of creation:||03 Jan 2013|
|Publication status:||Published in SIAM Journal on Financial Mathematics, SIAM, 2013, 4 (1), pp.1-25. <10.1137/110856605>|
|Note:||View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00552252v4|
|Contact details of provider:|| Web page: https://hal.archives-ouvertes.fr/|
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.:
- Burton Hollifield & Robert A. Miller & Patrik Sandås, 2004.
"Empirical Analysis of Limit Order Markets,"
Review of Economic Studies,
Oxford University Press, vol. 71(4), pages 1027-1063.
- Burton Hollifield & Robert Miller & Patrik Sandas, "undated". "Empirical Analysis of Limit Order Markets," GSIA Working Papers -290183991, Carnegie Mellon University, Tepper School of Business.
- Hollifield, Burton & Miller, Robert & Sandås, Patrik, 2001. "Empirical Analysis of Limit Order Markets," CEPR Discussion Papers 2843, C.E.P.R. Discussion Papers.
- Gourieroux, Christian & Jasiak, Joanna & Le Fol, Gaelle, 1999. "Intra-day market activity," Journal of Financial Markets, Elsevier, vol. 2(3), pages 193-226, August.
- Gaëlle Le Fol & Christian Gourieroux, 1999. "Intra-day market activity," Post-Print halshs-00536268, HAL.
- 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.
- Eric Smith & J. Doyne Farmer & Laszlo Gillemot & Supriya Krishnamurthy, 2002. "Statistical theory of the continuous double auction," Papers cond-mat/0210475, arXiv.org.
- Parlour, Christine A, 1998. "Price Dynamics in Limit Order Markets," Review of Financial Studies, Society for Financial Studies, vol. 11(4), pages 789-816.
- 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.
- Ioanid Rosu, 2009. "A Dynamic Model of the Limit Order Book," Post-Print hal-00515873, HAL.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
- 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. Full references (including those not matched with items on IDEAS)
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.