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A steady-state model of the continuous double auction

  • Hugh Luckock
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    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.

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    File URL: http://www.tandfonline.com/doi/abs/10.1088/1469-7688/3/5/305
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    Article provided by Taylor & Francis Journals in its journal Quantitative Finance.

    Volume (Year): 3 (2003)
    Issue (Month): 5 ()
    Pages: 385-404

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    Handle: RePEc:taf:quantf:v:3:y:2003:i:5:p:385-404
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    1. 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.
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    3. 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.
    4. 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.
    5. Mendelson, Haim, 1982. "Market Behavior in a Clearing House," Econometrica, Econometric Society, vol. 50(6), pages 1505-24, November.
    6. Eric Smith & J. Doyne Farmer & Laszlo Gillemot & Supriya Krishnamurthy, 2002. "Statistical theory of the continuous double auction," Papers cond-mat/0210475, arXiv.org.
    7. 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.
    8. Vernon L. Smith, 1962. "An Experimental Study of Competitive Market Behavior," Journal of Political Economy, University of Chicago Press, vol. 70, pages 322.
    9. Sugato Chakravarty & Craig Holden, 2002. "An Integrated Model of Market and Limit Orders," Finance 0201004, EconWPA.
    10. Glosten, Lawrence R, 1994. " Is the Electronic Open Limit Order Book Inevitable?," Journal of Finance, American Finance Association, vol. 49(4), pages 1127-61, September.
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