Forest-fire model as a supercritical dynamic model in financial systems.

Recently large-scale cascading failures in complex systems have garnered substantial attention. Such extreme events have been treated as an integral part of self-organized criticality (SOC). Recent empirical work has suggested that some extreme events systematically deviate from the SOC paradigm, requiring a different theoretical framework. We shed additional theoretical light on this possibility by studying financial crisis. We build our model of financial crisis on the well-known forest fire model in scale-free networks. Our analysis shows a nontrivial scaling feature indicating supercritical behavior, which is independent of system size. Extreme events in the supercritical state result from bursting of a fat bubble, seeds of which are sown by a protracted period of a benign financial environment with few shocks. Our findings suggest that policymakers can control the magnitude of financial meltdowns by keeping the economy operating within reasonable duration of a benign environment.