Bayesian Estimate of Default Probabilities via MCMC with Delayed Rejection

We develop a Bayesian hierarchical logistic regression model to predict the credit risk of companies classified in different sectors. Explanatory variables derived by experts from balance-sheets are included. Markov chain Monte Carlo (MCMC) methods are used to estimate the proposed model. In particular we show how the delaying rejection strategy outperforms the standard Metropolis-Hastings algorithm in terms of asymptotic efficiency of the resulting estimates. The advantages of our model over others proposed in the literature are discussed and tested via cross-validation procedures.