A hierarchical model of financial crashes

We follow up our previous conjecture that large stock market crashes are analogous to critical points in statistical physics. The term "critical" refers to regimes of cooperative behavior, such as magnetism at the Curie temperature and liquid-gas transitions, and is characterized by the singular mathematical behavior of relevant observables. To illustrate the concept of criticality, we present a simple hierarchical model of traders exhibiting "crowd" behavior and show that it has a well-defined critical point, whose mathematical signature is a power law dependence of the price, modulated by log-periodic structures, as recently found in marker data by several independent groups. (C) 1998 Elsevier Science B.V. All rights reserved.