A traffic lights approach to PD validation

As a consequence of the dependence experienced in loan portfolios, the standard binomial test which is based on the assumption of independence does not appear appropriate for validating probabilities of default (PDs). The model underlying the new rules for minimum capital requirements (Basle II) is taken as a point of departure for deriving two parametric test procedures that incorporate dependence effects. The first one makes use of the so-called granularity adjustment approach while the the second one is based on moment matching. The aim with this note is to present an approximate procedure for one-observation-based inference on the adequacy of probability of default (PD) forecasts. The PD forecast for a homogeneous portfolio of loans has to be compared to the realized default rate one year later. In case of independent default events, the natural procedure for this comparison would be the standard binomial test. However, the well-known fact that default events are correlated makes the binomial test appear unreliable. Our approach here is to model the dependent default events in a Basle II-like style and to arrive this way at a means to compute critical values which respect correlations. However, in the Basle II-model the distribution of default rates cannot be calculated with elementary arithmetic procedures as they are available for instance in MSExcel. Therefore we suggest two approximation schemes which seem to work with reasonable precision. ∗Deutsche Bundesbank, Postfach 10 06 02, 60006 Frankfurt am Main, Germany E-mail: [email protected] †The opinions expressed in this note are those of the author and do not necessarily reflect views shared by the Deutsche Bundesbank or its staff.