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Mean-field approximation for a limit order driven market model

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  • Frantisek Slanina
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    Abstract

    The mean-field variant of the model of limit order driven market introduced recently by Maslov is formulated and solved. The agents do not have any strategies and the memory of the system is kept within the order book. We show that he evolution of the order book is governed by a matrix multiplicative process. The resulting stationary distribution of step-to-step price changes is calculated. It exhibits a power-law tail with exponent 2. We obtain also the price autocorrelation function, which agrees qualitatively with the experimentally observed negative autocorrelation for short times.

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    File URL: http://arxiv.org/pdf/cond-mat/0104547
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number cond-mat/0104547.

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    Date of creation: Apr 2001
    Date of revision: Aug 2001
    Handle: RePEc:arx:papers:cond-mat/0104547

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    Web page: http://arxiv.org/

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    Cited by:
    1. 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.
    2. Jean-Philippe Bouchaud & Yuval Gefen & Marc Potters & Matthieu Wyart, 2003. "Fluctuations and response in financial markets: the subtle nature of `random' price changes," Papers cond-mat/0307332, arXiv.org, revised Aug 2003.
    3. Kostanjcar, Zvonko & Jeren, Branko & Juretic, Zeljan, 2012. "Impact of uncertainty in expected return estimation on stock price volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5563-5571.
    4. Szabolcs Mike & J. Doyne Farmer, 2007. "An empirical behavioral model of liquidity and volatility," Papers 0709.0159, arXiv.org.
    5. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frédéric Abergel, 2011. "Econophysics: agent-based models," Post-Print hal-00621059, HAL.
    6. 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.
    7. Biondi, Yuri & Giannoccolo, Pierpaolo & Galam, Serge, 2012. "Formation of share market prices under heterogeneous beliefs and common knowledge," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5532-5545.
    8. Maskawa, Jun-ichi, 2007. "Stock price fluctuations and the mimetic behaviors of traders," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 172-178.

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