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Importance of Positive Feedbacks and Over-confidence in a Self-Fulfilling Ising Model of Financial Markets

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  • Didier Sornette

    (CNRS-Univ. Nice and UCLA)

  • Wei-Xing Zhou

    (ECUST)

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    Abstract

    Following a long tradition of physicists who have noticed that the Ising model provides a general background to build realistic models of social interactions, we study a model of financial price dynamics resulting from the collective aggregate decisions of agents. This model incorporates imitation, the impact of external news and private information. It has the structure of a dynamical Ising model in which agents have two opinions (buy or sell) with coupling coefficients which evolve in time with a memory of how past news have explained realized market returns. We study two versions of the model, which differ on how the agents interpret the predictive power of news. We show that the stylized facts of financial markets are reproduced only when agents are over-confident and mis-attribute the success of news to predict return to herding effects, thereby providing positive feedbacks leading to the model functioning close to the critical point. Our model exhibits a rich multifractal structure characterized by a continuous spectrum of exponents of the power law relaxation of endogenous bursts of volatility, in good agreement with previous analytical predictions obtained with the multifractal random walk model and with empirical facts.

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    File URL: http://arxiv.org/pdf/cond-mat/0503607
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number cond-mat/0503607.

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    Date of creation: Mar 2005
    Date of revision: Mar 2005
    Publication status: Published in Physica A 370, 704-726 (2006)
    Handle: RePEc:arx:papers:cond-mat/0503607

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    Web page: http://arxiv.org/

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