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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)

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.

Suggested Citation

  • Didier Sornette & Wei-Xing Zhou, 2005. "Importance of Positive Feedbacks and Over-confidence in a Self-Fulfilling Ising Model of Financial Markets," Papers cond-mat/0503607, arXiv.org, revised Mar 2005.
  • Handle: RePEc:arx:papers:cond-mat/0503607
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. Torsten Trimborn & Philipp Otte & Simon Cramer & Max Beikirch & Emma Pabich & Martin Frank, 2018. "SABCEMM-A Simulator for Agent-Based Computational Economic Market Models," Papers 1801.01811, arXiv.org, revised Oct 2018.
    3. repec:eee:ecofin:v:42:y:2017:i:c:p:107-131 is not listed on IDEAS
    4. Shu-Heng Chen & Sai-Ping Li, 2011. "Econophysics: Bridges over a Turbulent Current," Papers 1107.5373, arXiv.org.
    5. Kei Katahira & Yu Chen, 2019. "Heterogeneous wealth distribution, round-trip trading and the emergence of volatility clustering in Speculation Game," Papers 1909.03185, arXiv.org.
    6. Kristoufek, Ladislav & Vošvrda, Miloslav S., 2016. "Herding, minority game, market clearing and efficient markets in a simple spin model framework," FinMaP-Working Papers 68, Collaborative EU Project FinMaP - Financial Distortions and Macroeconomic Performance: Expectations, Constraints and Interaction of Agents.
    7. Kei Katahira & Yu Chen & Gaku Hashimoto & Hiroshi Okuda, 2019. "Development of an agent-based speculation game for higher reproducibility of financial stylized facts," Papers 1902.02040, arXiv.org.
    8. Kaizoji, Taisei & Leiss, Matthias & Saichev, Alexander & Sornette, Didier, 2015. "Super-exponential endogenous bubbles in an equilibrium model of fundamentalist and chartist traders," Journal of Economic Behavior & Organization, Elsevier, vol. 112(C), pages 289-310.
    9. Chen, Shu-Heng & Chang, Chia-Ling & Tseng, Yi-Heng, 2014. "Social networks, social interaction and macroeconomic dynamics: How much could Ernst Ising help DSGE?," Research in International Business and Finance, Elsevier, vol. 30(C), pages 312-335.
    10. Ko, Bonggyun & Kim, Kyungwon, 2017. "Simulation of sovereign CDS market based on interaction between market participant," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 324-340.
    11. Maximilian Beikirch & Simon Cramer & Martin Frank & Philipp Otte & Emma Pabich & Torsten Trimborn, 2019. "Robust Mathematical Formulation of Agent-Based Computational Economic Market Models," Papers 1904.04951, arXiv.org, revised Nov 2019.
    12. repec:eee:phsmap:v:524:y:2019:i:c:p:503-518 is not listed on IDEAS
    13. Eckrot, A. & Jurczyk, J. & Morgenstern, I., 2016. "Ising model of financial markets with many assets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 250-254.
    14. Fang, Wen & Wang, Jun, 2013. "Fluctuation behaviors of financial time series by a stochastic Ising system on a Sierpinski carpet lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(18), pages 4055-4063.
    15. Zhang, Wei & Bi, Zhengzheng & Shen, Dehua, 2017. "Investor structure and the price–volume relationship in a continuous double auction market: An agent-based modeling perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 345-355.
    16. repec:eee:phsmap:v:493:y:2018:i:c:p:301-310 is not listed on IDEAS
    17. repec:eee:finlet:v:28:y:2019:i:c:p:348-354 is not listed on IDEAS
    18. Gusev, Maxim & Kroujiline, Dimitri & Govorkov, Boris & Sharov, Sergey V. & Ushanov, Dmitry & Zhilyaev, Maxim, 2014. "Predictable markets? A news-driven model of the stock market," MPRA Paper 58831, University Library of Munich, Germany.
    19. repec:eee:phsmap:v:517:y:2019:i:c:p:97-113 is not listed on IDEAS

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