In this thesis I describe the essential steps of developing a credit rating system. This comprises the credit scoring process that assigns a credit score to each credit, the forming of rating classes by the k-means algorithm and the assignment of a probability of default (PD) for the rating classes. The main focus is on the PD estimation for which two approaches are presented. The first and simple approach in form of a calibration curve assumes independence of the defaults of different corporate credits. The second approach with mixture models is more realistic as it takes default dependence into account. With these models we can use an estimate of a country’s GDP to calculate an estimate for the Value-at-Risk of some credit portfolio.