Zero Recovery Default Cascades

Abstract

This chapter realizes the central aim of the book, which is to understand a simple class of cascades on financial networks as a generalization of percolation theory. The main results apply to random financial networks with locally tree-like independence and characterize zero-recovery default cascade equilibria as fixed points of certain cascade mappings. The proofs of the main results follow a new and distinctive template presented here for the first time, that has the important virtue that its logic extends to LTI financial networks of arbitrary complexity. Numerical computations, both large network analytics and finite Monte Carlo simulations, verify that essential characteristics such as cascade extent and cascade frequency can be derived from the properties of the cascade fixed points.