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A Nonlinear Super-Exponential Rational Model of Speculative Financial Bubbles

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  • D. Sornette

    (Univ. Nice/CNRS and UCLA)

  • J. V. Andersen

    (Univ. Nice/CNRS)

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    Abstract

    Keeping a basic tenet of economic theory, rational expectations, we model the nonlinear positive feedback between agents in the stock market as an interplay between nonlinearity and multiplicative noise. The derived hyperbolic stochastic finite-time singularity formula transforms a Gaussian white noise into a rich time series possessing all the stylized facts of empirical prices, as well as accelerated speculative bubbles preceding crashes. We use the formula to invert the two years of price history prior to the recent crash on the Nasdaq (april 2000) and prior to the crash in the Hong Kong market associated with the Asian crisis in early 1994. These complex price dynamics are captured using only one exponent controlling the explosion, the variance and mean of the underlying random walk. This offers a new and powerful detection tool of speculative bubbles and herding behavior.

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    File URL: http://arxiv.org/pdf/cond-mat/0104341
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number cond-mat/0104341.

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    Date of creation: Apr 2001
    Date of revision: Apr 2002
    Publication status: Published in Int. J. Mod. Phys. C 13 (2), 171-188 (2002)
    Handle: RePEc:arx:papers:cond-mat/0104341

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    Web page: http://arxiv.org/

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    References

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    1. J. Doyne Farmer, 1999. "Market Force, Ecology, and Evolution," Computing in Economics and Finance 1999 651, Society for Computational Economics.
    2. Challet, D. & Zhang, Y.-C., 1997. "Emergence of cooperation and organization in an evolutionary game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 246(3), pages 407-418.
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    Citations

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    Cited by:
    1. D. Sornette, 2008. "Nurturing breakthroughs: lessons from complexity theory," Journal of Economic Interaction and Coordination, Springer, vol. 3(2), pages 165-181, December.
    2. D. Sornette & R. Woodard, . "Financial Bubbles, Real Estate bubbles, Derivative Bubbles, and the Financial and Economic Crisis," Working Papers, ETH Zurich, Chair of Systems Design CCSS-09-003, ETH Zurich, Chair of Systems Design.
    3. Li Lin & Didier Sornette, 2009. "Diagnostics of Rational Expectation Financial Bubbles with Stochastic Mean-Reverting Termination Times," Papers 0911.1921, arXiv.org.
    4. John M. Fry, 2009. "Statistical modelling of financial crashes: Rapid growth, illusion of certainty and contagion," EERI Research Paper Series EERI_RP_2009_10, Economics and Econometrics Research Institute (EERI), Brussels.
    5. Georges Harras & Didier Sornette, 2008. "How to grow a bubble: A model of myopic adapting agents," Papers 0806.2989, arXiv.org, revised Nov 2010.
    6. Wei-Xing Zhou & Didier Sornette, 2002. "Non-Parametric Analyses of Log-Periodic Precursors to Financial Crashes," Papers cond-mat/0205531, arXiv.org.
    7. Chong, You Quan & Wang, Bin & Yue Tan, Gladys Li & Cheong, Siew Ann, 2014. "Diversified firms on dynamical supply chain cope with financial crisis better," International Journal of Production Economics, Elsevier, vol. 150(C), pages 239-245.
    8. John FRY, 2010. "Bubbles And Crashes In Finance: A Phase Transition From Random To Deterministic Behaviour In Prices," Journal of Applied Research in Finance Bi-Annually, ASERS Publishing, vol. 0(2), pages 131-137, December.
    9. D. Sornette & Y. Malevergne & J. F. Muzy, 2002. "Volatility fingerprints of large shocks: Endogeneous versus exogeneous," Papers cond-mat/0204626, arXiv.org.
    10. Fry, J. M., 2009. "Bubbles and contagion in English house prices," MPRA Paper 17687, University Library of Munich, Germany.
    11. W. -X. Zhou & D. Sornette, 2002. "Evidence of a Worldwide Stock Market Log-Periodic Anti-Bubble Since Mid-2000," Papers cond-mat/0212010, arXiv.org, revised Aug 2003.
    12. Yukalov, V.I. & Sornette, D. & Yukalova, E.P., 2009. "Nonlinear dynamical model of regime switching between conventions and business cycles," Journal of Economic Behavior & Organization, Elsevier, vol. 70(1-2), pages 206-230, May.

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