Estimating the Probability of Default for No-Default and Low-Default Portfolios

The paper proposes a sequential Bayesian updating approach to estimate default probabilities on rating grade level for no- and low-default portfolios.Bayesian sequential updating enables default probabilities to be obtained also for those rating grades for which no defaults have been observed.The advantage of this approach is that it preserves the rank order of rating grades in the case of no defaults. Rank preservation is not ensured when using an identical prior distribution across all rating grades. We discuss Bayesian sequential updating for the beta–binomial model and a model incorporating the asymptotic single-risk factor model of the Basel Accord. Practical aspects such as incorporating information from external sources and the margin of conservatism are addressed