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A multi-agent nonlinear Markov model of the order book

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  • Kirill Vaninsky
  • Stepan Myzuchka
  • Alexander Lukov
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    Abstract

    We introduce and treat rigorously a new multi-agent model of the order book (OB). Our model is designed to explain the collective behavior of the market when new information a?ecting the market arrives. Our model has two major features. First, it has two additional parameters which we call slow vari- ables. These parameters measure the mood of two groups of investors, namely, bulls and bears. Second, our model captures the interaction between trading agents and constitutes a nonlinear Markov process which exhibits long term cor- relations. We explain the intuition behind the equations and present numerical simulations which show that the behavior of our model is similar to the behavior of the real market.

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    File URL: http://arxiv.org/pdf/1208.3083
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1208.3083.

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    Date of creation: Aug 2012
    Date of revision: Dec 2013
    Handle: RePEc:arx:papers:1208.3083

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    Web page: http://arxiv.org/

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    1. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frederic Abergel, 2011. "Econophysics review: II. Agent-based models," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 11(7), pages 1013-1041.
    2. Ioanid Rosu, 2009. "A Dynamic Model of the Limit Order Book," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 22(11), pages 4601-4641, November.
    3. Marco Avellaneda & Sasha Stoikov, 2008. "High-frequency trading in a limit order book," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 8(3), pages 217-224.
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