Clustered Defaults

Defaults in a credit portfolio of many obligors or in an economy populated with firms tend to occur in waves, reflecting their sharing of common risk factors and/or having systemic linkages via credit chains. One popular approach to characterizing defaults in is the Poisson intensity model coupled with stochastic covariates. A constraining feature of such models is that defaults of different obligors are independent events after conditioning on the covariates, which makes them ill-suited for modeling clustered defaults. Although individual default intensities under such models can be high and correlated via the stochastic covariates, joint default rates will always be zero, because the joint default probabilities are in the order of the length of time squared or higher. In this paper, we develop a hierarchical intensity model with three layers of shocks – common, group-specific and individual. When a common (or group-specific) shock occurs, all obligors (or group members) face individual default probabilities, determining whether they actually default. The likelihood function of this hierarchical intensity model is derived and can be used to estimate the model parameters. A convolution-based algorithm is also developed for obtaining the predicted default distribution, which is useful for credit portfolio analysis. This new model is implemented on the US corporate default/bankruptcy data and found to be superior to the standard intensity model