Bayesian Variable Selection and Model Averaging for modelling the Probability of Default of mortgage portfolios

The subjective choice of which variables should be included in a Probability of Default (PD) model of a mortgage portfolio can significantly influence the outcome of the prediction. Bayesian Variable Selection (BVS) can be used to objectively estimate which variables should be included in the model, by assigning posterior probabilities to different variable combinations. Bayesian Model Averaging (BMA) can be used to average between these different combinations with the aim of decreasing the model specific errors. This paper investigates the improvements in prediction performance of PD models that can be achieved by implementing BVS and BMA. It is shown that BVS outperforms the benchmark variable selection criteria. It follows that implementing BMA results in an accuracy loss compared to specific BVS models, but results in more stability, robustness and overall more accurate predictions for selected model combinations.