Mixture Models

Current credit risk models can be divided into two classes. On the one hand there are latent variable or threshold models where default occurs when a latent variable (e.g. the firm’s asset value) falls below some threshold. Examples for this class of credit risk models are the theoretical Merton model and, based on this, also important industry models like KMV’s Portfolio Manager or the CreditMetrics Model. We studied these types of models in some detail in Chapter 3. On the other hand there are mixture models where the default probabilities of different obligors are assumed to depend on some common economic factors. These models can be treated as two stage models. Conditional on the realization of economic factors the individual default probabilities are assumed to be independent whereas they can be unconditionally dependent. The conditional default probabilities are modeled as random variables with some mixing distribution which is specified in a second step. This class of credit risk models will be treated in this chapter. A prominent example of such a mixture model is the CreditRisk⁺ model which we will discuss in more detail in Chapter 6.