Comparing lifetime estimates of probability of default for refinancing operations with survival analysis and ensemble methods

Abstract

We compare different models on estimating the probability of default over a time horizon, considering censored data. Models were fitted from a survival analysis perspective, considering both classic models (Cox Proportional Hazard) with penalized variations and ensemble machine learning methods (boosting and bagging). Using a dataset of credit card refinancing operations, we assess accuracy performance in both out-of-sample and out-of-time observations. We assess well-established metrics, such as the concordance index, and measures that indicate calibration power (integrated Brier score and time-dependent dynamic AUC). Results show that a boosting approach with component-wise regression as base learner outperform other models for short term operations (36 months), in contrast to longer term transactions (60 months), where Cox Proportional Hazard (with and without penalization) depicted better results.