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