Inhomogeneous financial networks and contagious links

We propose a framework for testing the possibility of large cascades in financial networks. This framework accommodates a variety of specifications for the probabilities of emergence of "contagious links" conditional on a macroeconomic shock, where a contagious link leads to the default of a bank following the default of its counterparty. Under general contagion mechanisms and incomplete information, the financial network is modeled as an inhomogeneous random graph, where the conditional probabilities of having contagious links depend on banks' characteristics. We give different bounds on the size of the cascade through contagious links and derive testable conditions for this cascade to be small.