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Low-traffic limit and first-passage times for a simple model of the continuous double auction

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  • Scalas, Enrico
  • Rapallo, Fabio
  • Radivojević, Tijana

Abstract

We consider a simplified model of the continuous double auction where prices are integers varying from 1 to N with limit orders and market orders, but quantity per order limited to a single share. For this model, the order process is equivalent to two M∕M∕1 queues. We study the behavior of the auction in the low-traffic limit where limit orders are immediately matched by market orders. In this limit, the distribution of prices can be computed exactly and gives a reasonable approximation of the price distribution when the ratio between the rate of order arrivals and the rate of order executions is below 1∕2. This is further confirmed by the analysis of the first-passage time in 1 or N.

Suggested Citation

  • Scalas, Enrico & Rapallo, Fabio & Radivojević, Tijana, 2017. "Low-traffic limit and first-passage times for a simple model of the continuous double auction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 485(C), pages 61-72.
    • Handle: RePEc:eee:phsmap:v:485:y:2017:i:c:p:61-72
    DOI: 10.1016/j.physa.2017.05.020
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    References listed on IDEAS

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    1. Tijana Radivojević & Jonatha Anselmi & Enrico Scalas, 2012. "A stylized model for the continuous double auction," Lecture Notes in Economics and Mathematical Systems, in: Andrea Teglio & Simone Alfarano & Eva Camacho-Cuena & Miguel Ginés-Vilar (ed.), Managing Market Complexity, edition 127, chapter 0, pages 115-125, Springer.
    2. 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.
    3. B. Tóth & E. Scalas & J. Huber & M. Kirchler, 2007. "The value of information in a multi-agent market model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 55(1), pages 115-120, January.
    4. Scalas, Enrico & Kaizoji, Taisei & Kirchler, Michael & Huber, Jürgen & Tedeschi, Alessandra, 2006. "Waiting times between orders and trades in double-auction markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 463-471.
    5. Rama Cont & Adrien De Larrard, 2012. "Order book dynamics in liquid markets: limit theorems and diffusion approximations," Papers 1202.6412, arXiv.org.
    6. Rama Cont & Adrien de Larrard, 2013. "Price Dynamics in a Markovian Limit Order Market," Post-Print hal-00552252, HAL.
    7. Gode, Dhananjay K & Sunder, Shyam, 1993. "Allocative Efficiency of Markets with Zero-Intelligence Traders: Market as a Partial Substitute for Individual Rationality," Journal of Political Economy, University of Chicago Press, vol. 101(1), pages 119-137, February.
    8. Jose Blanchet & Xinyun Chen, 2013. "Continuous-time Modeling of Bid-Ask Spread and Price Dynamics in Limit Order Books," Papers 1310.1103, arXiv.org.
    9. Marco Raberto & Fabio Rapallo & Enrico Scalas, 2011. "Semi-Markov Graph Dynamics," PLOS ONE, Public Library of Science, vol. 6(8), pages 1-13, August.
    10. Bondesson, Lennart, 1991. "A characterization of first passage time distributions for random walks," Stochastic Processes and their Applications, Elsevier, vol. 39(1), pages 81-88, October.
    11. Bottazzi, Giulio & Dosi, Giovanni & Rebesco, Igor, 2005. "Institutional architectures and behavioral ecologies in the dynamics of financial markets," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 197-228, February.
    12. Tijana Radivojević & Jonatha Anselmi & Enrico Scalas, 2014. "Ergodic Transition in a Simple Model of the Continuous Double Auction," PLOS ONE, Public Library of Science, vol. 9(2), pages 1-5, February.
    13. Anufriev, Mikhail & Panchenko, Valentyn, 2009. "Asset prices, traders' behavior and market design," Journal of Economic Dynamics and Control, Elsevier, vol. 33(5), pages 1073-1090, May.
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