11.6 Static Reduced Form Models—CreditRisk+
The threshold models from the previous section construct the default process from underlying financial and economic variables, and can thus be called structural models. An alternative is simply to assume a form for the default distribution rather than deriving the parameters from first principles, and then fit the parameters of the distribution to data. Such models are termed reduced form models. The reduced form approach has some advantages: the default process can be flexibly specified, both to fit observed data but also for analytical tractability. CreditRisk+, developed by Credit Suisse Financial Products in the 1990s (see Credit Suisse Financial Products 1997) is an industry example of a reduced form model.
CreditRisk+ concentrates on default (not credit rating migration) and the default and loss distribution for a portfolio. The mathematical form assumed for the individual-firm default process is reasonable and, importantly, leads to a convenient and tractable default distribution. Unlike the MKMV and CreditMetrics approaches outlined earlier, which require time-consuming simulation, the CreditRisk+ model can be solved relatively easily without simulation. This is a considerable advantage.26
The CreditRisk+ model focuses on two attributes of the default process:
1. Default rate or intensity, the analogue of probability of default in the models discussed earlier.
2. Variability in default intensities, although it is really the common ...