  In this work we provide a simple setting that connects the structural
modelling approach of Gai-Kapadia interbank networks with the mean-field
approach to default contagion. To accomplish this we make two key
contributions. First, we propose a dynamic default contagion model with
endogenous early defaults for a finite set of banks, generalising the
Gai-Kapadia framework. Second, we reformulate this system as a stochastic
particle system leading to a limiting mean-field problem. We study the
existence of these clearing systems and, for the mean-field problem, the
continuity of the system response.
