Eur. Phys. J. B 79, 91-98 (2011)
https://doi.org/10.1140/epjb/e2010-10668-8

Self-organized model of cascade spreading

Physics Department, University of Fribourg, 1700 Fribourg, Switzerland

Corresponding author: ^a matus.medo@unifr.ch

Received: 31 August 2010
Revised: 9 November 2010
Published online: 21 December 2010

Abstract

We study simultaneous price drops of real stocks and show that for high drop thresholds they follow a power-law distribution. To reproduce these collective downturns, we propose a minimal self-organized model of cascade spreading based on a probabilistic response of the system elements to stress conditions. This model is solvable using the theory of branching processes and the mean-field approximation. For a wide range of parameters, the system is in a critical state and displays a power-law cascade-size distribution similar to the empirically observed one. We further generalize the model to reproduce volatility clustering and other observed properties of real stocks.