Large Financial Crashes

Paper Abstract:

“We propose that large stock market crashes are analogous to critical points studied in statistical physics with log-periodic correction to scaling. We extend our previous renormalization group model of stock market prices prior to and after crashes [D. Sornette et al., J.Phys.l France 6, 167, 1996] by including the first non-linear correction. This predicts the existence of a log-frequency shift over time in the log-periodic oscillations prior to a crash. This is tested on the two largest historical crashes of the century, the october 1929 and october 1987 crashes, by fitting the stock market index over an interval of 8 years prior to the crashes. The good quality of the fits, as well as the consistency of the parameter values obtained from the two crashes, promote the theory that crashes have their origin in the collective ‘”crowd” behavior of many interacting agents.”

The authors conclusion for the overall herding phenomena within financial markets:

“Stock markets are fascinating structures with analogies to what is arguably the most complex dynamical system found in natural sciences, i.e., the human mind. Instead
of the usual interpretation of the Efficient Market Hypothesis in which traders extract and incorporate consciously (by their action) all information contained in market prices, we propose that the market as a whole can exhibit an “emergent” behavior not shared by any of its constituents. In other words, we have in mind the process of the emergence of intelligent behavior at a macroscopic scale that individuals at the microscopic scales have no idea of. This process has been discussed in biology for instance in the animal populations such as ant colonies or in connection with the emergence of consciousness.”