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.Comment: 8 pages, 6 figure