Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2001-04-18
Int. J. Mod. Phys. C 13 (2), 171-188 (2002)
Physics
Condensed Matter
Statistical Mechanics
Latex document of 24 pages including 5 eps figures
Scientific paper
10.1142/S0129183102003085
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.
Andersen Jorgen Vitting
Sornette Didier
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