I am working with a UK credit-union and we are looking to build a model to assess our credit risk and changes to this over time. We have a number of loans to borrowers who each have a credit rating (lets say these are banded A, AA, AAA, B, BBB, etc...).
The way I have proceeded so far is to get the history of defaults in each rating band and build a conjugate model (Gamma/Poisson) to measure the risk profile of each band. I can then use the expected default and variance to build up some measure of expected loss, risk profiles, confidence levels, etc....
The loans are to individual members and as the credit union is not tied to a specific organisation/industry I have treated the individual loans as independent and identically distributed with no strong, identifiable correlation.
One factor that worries me is that some members might have abnormally higher loan balances than others. Say, for example I have 300 loans in category B that average £500, but I have 15 loans in category AAA that average £10,000. The exposure in each category is the same, but as the average loan per borrower is higher in one category, should I recognize in my model that a few defaults in this category will have a larger financial effect than a higher number of defaults in the other category? If so, how can I model this? Is a simple Poisson model acceptable for this?
I guess I'm asking how I should treat concentration factors when I'm currently assessing the risk as if its homogeneous with regard the borrowers and the amounts the borrow. Any help would be very welcome!