In the latest NAG technical report we examine the main theoretical aspects in some models used in Portfolio credit risk. We introduce the well-known Vasicek model, the large homogeneous portfolios or Vasicek distribution and their corresponding generalizations. An illustrative example considering factors following a logistic distribution is presented. Numerical experiments for several homogeneous portfolios are performed in order to compare these methods. Finally, we use the NAG Toolbox for MATLAB® for implementing prototypes of these models quickly.
We described the most widely used models for the calculation of default probabilities in portfolio credit risk. We introduced the Vasicek one-factor model and its generalization for factors following non Normal distributions. Similarly, we presented the large portfolio approximation method and we generated closed-form expressions for the so-called general loss distribution. In section 7 we provide code for the main routines used throughout this technical report. The code is not designed to be fast, but to serve as a guidance and point of departure for more elaborate implementations. Furthermore, the code can be easily extended to heterogeneous portfolios. As shown, only a few lines of code using the NAG Toolbox for MATLAB are required to implement the studied models, which makes it extraordinarily suitable for prototyping.
You can read the report here.