Default Clustering In Large Portfolios: Typical And Atypical Events

The authors develop a dynamic point process model of correlated default timing in a portfolio of firms, and analyze typical and atypical default profiles in the limit as the size of the pool grows. In the model, a name defaults at a stochastic intensity that is influenced by an idiosyncratic risk process, a systematic risk process common to all names, and past defaults. They prove a law of large numbers for the default rate in the pool, which describes the "Typical" behavior of defaults. Large deviation arguments are then used to identify the way that atypically large (i.e., "Rare") default clusters are most likely to occur. The results give insights into how different sources of default correlation interact to generate excessive portfolio losses.