In this chapter we dealt with validation of rating systems, constructed to forecast a 1-year probability of default. Hereby, we focused on statistical tests and their application for bank internal purposes, especially in the Basel II periphery. We built up a simulation based framework to take account of dependencies in defaults (asset correlation), which additionally has the potential to appraise the type II error, i.e. the non-detection of a bad rating system, for optional scenarios. Hereby, the well known exact and approximated binomial test and the Hosmer-Lemeshow-
test are used, but we also introduced the less popular Spiegelhalter test and an approach called simultaneous binomial test, which allow the testing of a complete rating system and not just each grade separately. As it is important for banks to compare the quality of modules of their rating system, we also refer to the Redelmeier test. As for any applied statistical method, building test samples is an important issue. We designed the concept of “the rolling 12-months-window” to fulfil the Basel II and bank’s internal risk management requirements as well as using the bank’s IT-environment (rating database) effectively and is in harmony with our definition of what a rating should reflect, namely the bank’s most accurate assessment of the 1-year-PD of a borrower. All concepts are demonstrated with a very up-to-date, real-life bank internal rating data set in detail.
We focus mainly on statistical concepts for rating validation (backtesting) but it has to be emphasised that for a comprehensive and adequate validation in the spirit of Basel II, much more is required. To name a few, these include adherence of defined bank internal rating processes, accurate and meaningful use of ratings in the bank’s management systems and correct implementation in the IT-environment.