Large financial crashes

TL;DR

This paper models large stock market crashes as critical phenomena with log-periodic oscillations, extending previous physics-inspired models to include non-linear corrections and testing them on historical crashes.

Contribution

It introduces a non-linear correction to the renormalization group model of stock market crashes, predicting a log-frequency shift in pre-crash oscillations and validating it with historical data.

Findings

Good fit of the model to 1929 and 1987 crashes

Parameter consistency across different crashes

Supports collective behavior as crash origin

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.I 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.