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

  • Didier Sornette

    (CNRS-Univ. Nice and UCLA)

  • Wei-Xing Zhou

    (ECUST)

Registered author(s):

    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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    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
    Contact details of provider: Web page: http://arxiv.org/

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    1. Lux, T. & M. Marchesi, . "Volatility Clustering in Financial Markets: A Micro-Simulation of Interacting Agents," Discussion Paper Serie B 437, University of Bonn, Germany, revised Jul 1998.
    2. Hommes, C.H., 2000. "Financial Markets as Nonlinear Adaptive Evolutionary Systems," CeNDEF Working Papers 00-03, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    3. Steven N. Durlauf, 1991. "Nonergodic Economic Growth," NBER Working Papers 3719, National Bureau of Economic Research, Inc.
    4. Fabrizio Lillo & J. Doyne Farmer & Rosario N. Mantegna, 2002. "Single Curve Collapse of the Price Impact Function for the New York Stock Exchange," Papers cond-mat/0207428, arXiv.org.
    5. Blume Lawrence E., 1995. "The Statistical Mechanics of Best-Response Strategy Revision," Games and Economic Behavior, Elsevier, vol. 11(2), pages 111-145, November.
    6. L. Blume, 2010. "The Statistical Mechanics of Strategic Interaction," Levine's Working Paper Archive 488, David K. Levine.
    7. repec:att:wimass:9621 is not listed on IDEAS
    8. J. Doyne Farmer, 2002. "Market force, ecology and evolution," Industrial and Corporate Change, Oxford University Press, vol. 11(5), pages 895-953, November.
    9. Gaunersdorfer, Andrea, 2000. "Endogenous fluctuations in a simple asset pricing model with heterogeneous agents," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 799-831, June.
    10. Rama Cont & Jean-Philippe Bouchaud, 1997. "Herd behavior and aggregate fluctuations in financial markets," Science & Finance (CFM) working paper archive 500028, Science & Finance, Capital Fund Management.
    11. Durlauf, Steven N, 1996. " A Theory of Persistent Income Inequality," Journal of Economic Growth, Springer, vol. 1(1), pages 75-93, March.
    12. Steven N. Durlauf, 1991. "Multiple Equilibria and Persistence in Aggregate Fluctuations," NBER Working Papers 3629, National Bureau of Economic Research, Inc.
    13. Yanhui Liu & Parameswaran Gopikrishnan & Pierre Cizeau & Martin Meyer & Chung-Kang Peng & H. Eugene Stanley, 1999. "The statistical properties of the volatility of price fluctuations," Papers cond-mat/9903369, arXiv.org, revised Mar 1999.
    14. J-F. Muzy & D. Sornette & J. delour & A. Arneodo, 2001. "Multifractal returns and hierarchical portfolio theory," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 131-148.
    15. Sato, Aki-Hiro & Takayasu, Hideki, 1998. "Dynamic numerical models of stock market price: from microscopic determinism to macroscopic randomness," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 250(1), pages 231-252.
    16. William A. Brock & Blake D. LeBaron, 1995. "A Dynamic Structural Model for Stock Return Volatility and Trading Volume," NBER Working Papers 4988, National Bureau of Economic Research, Inc.
    17. Heath, Chip & Gonzalez, Rich, 1995. "Interaction with Others Increases Decision Confidence but Not Decision Quality: Evidence against Information Collection Views of Interactive Decision Making," Organizational Behavior and Human Decision Processes, Elsevier, vol. 61(3), pages 305-326, March.
    18. Taisei Kaizoji & Stefan Bornholdt & Yoshi Fujiwara, 2002. "Dynamics of price and trading volume in a spin model of stock markets with heterogeneous agents," Papers cond-mat/0207253, arXiv.org.
    19. Jean-Philippe Bouchaud & Rama Cont, 1998. "A Langevin approach to stock market fluctuations and crashes," Science & Finance (CFM) working paper archive 500027, Science & Finance, Capital Fund Management.
    20. Matthieu Wyart & Jean-Philippe Bouchaud, 2003. "Self-referential behaviour, overreaction and conventions in financial markets," Science & Finance (CFM) working paper archive 500020, Science & Finance, Capital Fund Management.
    21. Lux, Thomas, 1995. "Herd Behaviour, Bubbles and Crashes," Economic Journal, Royal Economic Society, vol. 105(431), pages 881-96, July.
    22. M. Pasquini & M. Serva, 2000. "Clustering of volatility as a multiscale phenomenon," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 16(1), pages 195-201, July.
    23. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
    24. Vasiliki Plerou & Parameswaran Gopikrishnan & Xavier Gabaix & H. Eugene Stanley, 2001. "Quantifying Stock Price Response to Demand Fluctuations," Papers cond-mat/0106657, arXiv.org.
    25. B. M. Roehner & D. Sornette, 2000. ""Thermometers" of Speculative Frenzy," Papers cond-mat/0001353, arXiv.org.
    26. Y. Malevergne & V. F. Pisarenko & D. Sornette, 2003. "Empirical Distributions of Log-Returns: between the Stretched Exponential and the Power Law?," Papers physics/0305089, arXiv.org.
    27. Welch, Ivo, 1992. " Sequential Sales, Learning, and Cascades," Journal of Finance, American Finance Association, vol. 47(2), pages 695-732, June.
    28. Brock,W.A. & Hommes,C.H., 1998. "Rational animal spirits," Working papers 23, Wisconsin Madison - Social Systems.
    29. Cont, Rama & Bouchaud, Jean-Philipe, 2000. "Herd Behavior And Aggregate Fluctuations In Financial Markets," Macroeconomic Dynamics, Cambridge University Press, vol. 4(02), pages 170-196, June.
    30. Lux, T. & M. Marchesi, . "Scaling and Criticality in a Stochastic Multi-Agent Model of a Financial Market," Discussion Paper Serie B 438, University of Bonn, Germany, revised Jul 1998.
    31. Kempf, Alexander & Korn, Olaf, 1999. "Market depth and order size1," Journal of Financial Markets, Elsevier, vol. 2(1), pages 29-48, February.
    32. Bikhchandani, Sushil & Hirshleifer, David & Welch, Ivo, 1992. "A Theory of Fads, Fashion, Custom, and Cultural Change in Informational Cascades," Journal of Political Economy, University of Chicago Press, vol. 100(5), pages 992-1026, October.
    33. Potters, Marc & Bouchaud, Jean-Philippe, 2003. "More statistical properties of order books and price impact," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 133-140.
    34. Sornette, D & Helmstetter, A, 2003. "Endogenous versus exogenous shocks in systems with memory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 318(3), pages 577-591.
    35. Stauffer, Dietrich & Sornette, Didier, 1999. "Self-organized percolation model for stock market fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 271(3), pages 496-506.
    36. Lux, Thomas, 1998. "The socio-economic dynamics of speculative markets: interacting agents, chaos, and the fat tails of return distributions," Journal of Economic Behavior & Organization, Elsevier, vol. 33(2), pages 143-165, January.
    37. W. A. Brock, 1993. "Pathways to Randomness in the Economy: Emergent Nonlinearity and Chaos in Economics and Finance," Working Papers 93-02-006, Santa Fe Institute.
    38. A. Bershadskii, 1999. "Multifractal critical phenomena in traffic and economic processes," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 11(2), pages 361-364, September.
    39. 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.
    40. Youssefmir, Michael & Huberman, Bernardo A & Hogg, Tad, 1998. "Bubbles and Market Crashes," Computational Economics, Society for Computational Economics, vol. 12(2), pages 97-114, October.
    41. Adlai Fisher & Laurent Calvet & Benoit Mandelbrot, 1997. "Multifractality of Deutschemark/US Dollar Exchange Rates," Cowles Foundation Discussion Papers 1166, Cowles Foundation for Research in Economics, Yale University.
    42. Ide, Kayo & Sornette, Didier, 2002. "Oscillatory finite-time singularities in finance, population and rupture," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 307(1), pages 63-106.
    43. LeBaron, Blake, 2000. "Agent-based computational finance: Suggested readings and early research," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 679-702, June.
    44. Brock, William A. & Hommes, Cars H., 1998. "Heterogeneous beliefs and routes to chaos in a simple asset pricing model," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1235-1274, August.
    45. Sieck, Winston & Yates, J. Frank, 1997. "Exposition Effects on Decision Making: Choice and Confidence in Choice," Organizational Behavior and Human Decision Processes, Elsevier, vol. 70(3), pages 207-219, June.
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