SummaryReliable estimation of the probability of default (PD) of a customer is one of the most important tasks in credit risk modelling for banks applying the internal ratings-based approach under the Basel II–III framework. Motivated by the desire to analyse reliably a low default portfolio of non-profit housing companies, we consider PD estimation within a Bayesian framework and develop objective priors for the parameter θ representing the PD in the Gaussian and the Student t single-factor models. A marginal reference prior and limiting versions of it are presented and their posterior propriety is studied. The priors are shown to be direct generalizations of the Jeffreys prior in the binomial model. We use Markov chain Monte Carlo strategies to sample efficiently from the posterior distributions and compare the developed priors on the grounds of the frequentist properties of the resulting Bayesian inferences with subjective priors previously proposed in the literature. Finally, the analysis of the non-profit housing companies portfolio highlights the ultility of the methodological developments.