For market risk models the concept of backtesting involves the whole model, whereas in the internal ratings-based approach of Basel II validation procedures restrict to the three model inputs: probability of default, exposure at default and loss given default. As an enlargement of this concept procedures are proposed which simultaneously use the three model inputs. The proposed tests for the expected loss, the unexpected loss, the value-at-risk, and for the economical capital implicitly take into account the interaction between granularity and correlation. The problem of estimating default correlations using external rating data is addressed. Estimated correlations from a large retail data set are presented.
