2025/05/02 by Arno Botha, Botha, Arno, Tanja Verster +3 · 1 voice
Economics, Econometrics and Finance · Mathematics · #Applications (stat.AP) #FOS: Computer and information sciences #FOS: Economics and business #Risk Management (q-fin.RM) #Statistical Finance (q-fin.ST) #q-fin.RM #q-fin.ST #stat.AP
paper · pdf · doi:10.48550/arxiv.2505.01044
arxiv published 2025/05/02 · arxiv updated 2026/01/28
In the pursuit of modelling a loan's probability of default (PD) over its lifetime, repeat default events are often ignored when using Cox Proportional Hazard (PH) models. Excluding such events may produce biased and inaccurate PD-estimates, which can compromise financial buffers against future losses. Accordingly, we investigate a few subtypes of Cox-models that can incorporate recurrent default events. We explore both the Andersen-Gill (AG) and the Prentice-Williams-Peterson (PWP) spell-time models using real-world data as an illustration. These models are compared against a baseline that deliberately ignores recurrent events, called the time to first default (TFD) model. Our models are evaluated using Harrell's c-statistic, adjusted Cox-Sell residuals, and a novel extension of time-dependent receiver operating characteristic analysis. From these Cox-models, we demonstrate how to derive a portfolio-level term-structure of default risk, which is a series of marginal PD-estimates over the average loan's lifetime. While the TFD- and PWP-models do not differ significantly across all diagnostics, the AG-model underperformed expectations. We believe that our pedagogical tutorial, as accompanied by a codebase, would be of great value to practitioner and regulator alike. Accordingly, our work enhances the current practice of using Cox-modelling in producing timeous and accurate PD-estimates under IFRS 9.