The Default Cascade Process in Stochastic Financial Networks

Abstract

We introduce and study the following default cascade process in stochastic financial networks.

We consider a finite set of agents, holding claims on each other, who meet and interact pairwise with their counterparties at random times (agents meet at times of a Poisson process) and, upon meeting, update their states. If, at the meeting time, the debtor agent is solvent, the two agents continue to meet and interact. Otherwise, when a defaulted debtor agent meets its creditor agent, the creditor agent receives a random loss with distribution depending on its characteristics. In this case, the two agents stop meeting each other.

Our main result consists of a precise asymptotic expression for the fraction of defaulted agents at any time, in the case of heterogeneous random financial networks, where agents meet counterparties in a sparse directed random graph, and when the meeting times are i.i.d. exponential random variables.

Keywords: Financial Networks, Systemic Risk, Default Cascade Process, Limit Theorems.

JEL Classification: G01, G28