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This work has the objective of estimating default probabilities andcorrelations of credit portfolios given default rate information through aBayesian framework using Stan. We use Vasicek's single factor credit model toestablish the theoretical framework for the behavior of the default rates, anduse NUTS Markov Chain Monte Carlo to estimate the parameters. We compare theBayesian estimates with classical estimates such as moments estimators andmaximum likelihood estimates. We apply the methodology both to simulated dataand to corporate default rates, and perform inferences through Bayesian methodsin order to exhibit the advantages of such a framework. We perform defaultforecasting and exhibit the importance of an adequate estimation of defaultcorrelations, and exhibit the advantage of using Stan to perform samplingregarding prior choice.

Estimating Default Probability and Correlation using Stan