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A Nonlinear Super-Exponential Rational Model of Speculative Financial Bubbles

  • D. Sornette

    (Univ. Nice/CNRS and UCLA)

  • J. V. Andersen

    (Univ. Nice/CNRS)

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

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    1. J. Doyne Farmer, 2002. "Market force, ecology and evolution," Industrial and Corporate Change, Oxford University Press, vol. 11(5), pages 895-953, November.
    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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