The Term Structure of Default Probabilities

Accounting standards require that financial institutions must measure default risk with respect to the full maturity of a financial instrument. This requires forecasting of future default probabilities. The forecast of future default probabilities concerns two aspects: forecasting macroeconomic scenarios and future average (with respect to the macro-economy) default probabilities. The present paper addresses the modelling of future average default probabilities. Due to the small number of defaults and observations this poses a difficult problem in the corporate area and requires a parsimonious model to deal with the sparse data situation. The degree of difficulty is made greater by the fact that default probabilities change for corporations via different patterns over time, with the pattern being depend on the initial rating grade. For initial investment-grade ratings the risk of a default increases, while for the bottom of the rating scale default probabilities decrease. To model these different patterns the paper proposes to extend the existing discrete-time survival model and to incorporate an additional time- and co-variate-dependent shape parameter into the hazard function. Using data from Standard & Poor's the paper shows that the shape parameter is able to reproduce the different patterns. The proposed model is bench-marked against a model which does not employ a shape parameter and the results show that the shape parameter improves in-sample and out-of-sample prediction