As an example of A-IRB model, in this class we consider Credit Risk Plus © (CR+) by Credit Suisse.
Introduced in 1997, CR+ is a rather powerful model, which allows for the modeling of complex portfolios of instruments.

CR+ is not a structural model of default, but rather a mixture model.
In mixture models, the default probabilities of a set of n obligors are considered to be conditionally independent, given a vector of common economic factors. In CR+ default probabilities are conditionally Poisson distributed.

The study of mixture models is very interesting from a probabilistic point of view, but it is too complex for a course at this level, called “An introduction to Credit Risk Management”.

In this class, we will just see the basic idea behind Credit Risk Plus. And we will see that in this model we can explicitly compute the (expected) loss distribution of an entire portfolio, so that we are able to compute C-VaR, ES and all the other quantities we are interested in, in order to obtain RWA and capital requirements.

This implies that, when using a model like CR+, we are under the A-IRB approach. If the regulator agrees with our use of the model, we are not supposed to use risk-weight functions or other similar objects. We just compute capital requirements using our own model.