Calibration of Internal Rating Systems : The Case of Dependent Default Events

We compare four different test approaches for the calibration quality of internal rating systems in the case of dependent default events. Two of them are approximation approaches and two are simulation approaches of one- and multi-factor models. We find that multi-factor models generate more precise results through lower upper bound default rates and narrower confidence intervals. For confidence levels of 95%, the approximation approaches overestimate the upper bound default rates. For low asset correlation, especially for less than 0.5%, the granularity adjustment approach does not deliver reasonable results. For low numbers of debtors, the approximation approaches sharply overestimate the upper bound default rates. Using empirical inter-factor correlations we find that confidence intervals of two-factor models are much tighter compared with the one-factor model