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Dynamical Trading Mechanism in Limit Order Markets

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  • Shilei Wang
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    Abstract

    This work's purpose is to understand the dynamics of limit order books in order-driven markets. We try to illustrate a dynamical trading mechanism attached to the microstructure of limit order markets. We capture the iterative nature of trading processes, which is critical in the dynamics of bid-ask pairs and the switching laws between different traders' types and their orders. In general, after introducing the atomic trading scheme, we study a general iterated trading process in both combinatorial and stochastic ways, and state a few results on the stability of a dynamical trading system. We also study the controlled dynamics of the spread and the mid-price in an iterated trading system, when their movements, generated from the dynamics of bid-ask pairs, are assumed to be restricted within some extremely small ranges.

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    File URL: http://arxiv.org/pdf/1303.3133
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1303.3133.

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    Date of creation: Mar 2013
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    Publication status: Published in Algorithm. Finance 2 (2013), no. 3-4, 213-231
    Handle: RePEc:arx:papers:1303.3133

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    Web page: http://arxiv.org/

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    1. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-35, November.
    2. J. Doyne Farmer & Paolo Patelli & Ilija I. Zovko, 2003. "The Predictive Power of Zero Intelligence in Financial Markets," Papers cond-mat/0309233, arXiv.org, revised Feb 2004.
    3. Foucault, Thierry & Kadan, Ohad & Kandel, Eugene, 2001. "Limit Order Book as a Market for Liquidity," CEPR Discussion Papers 2889, C.E.P.R. Discussion Papers.
    4. Bruce N. Lehmann and David M. Modest., 1994. "Trading and Liquidity on the Tokyo Stock Exchange: A Bird's Eye View," Research Program in Finance Working Papers RPF-234, University of California at Berkeley.
    5. Lawrence R. Glosten & Paul R. Milgrom, 1983. "Bid, Ask and Transaction Prices in a Specialist Market with Heterogeneously Informed Traders," Discussion Papers 570, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    6. Parlour, Christine A, 1998. "Price Dynamics in Limit Order Markets," Review of Financial Studies, Society for Financial Studies, vol. 11(4), pages 789-816.
    7. Harris, Lawrence & Hasbrouck, Joel, 1996. "Market vs. Limit Orders: The SuperDOT Evidence on Order Submission Strategy," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 31(02), pages 213-231, June.
    8. 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.
    9. Lehmann, Bruce N & Modest, David M, 1994. " Trading and Liquidity on the Tokyo Stock Exchange: A Bird's Eye View," Journal of Finance, American Finance Association, vol. 49(3), pages 951-84, July.
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