Towards modelling lifetime default risk: Exploring different subtypes of recurrent event Cox-regression models

2025-05-02

AI Summary

Under IFRS 9, traditional probability-of-default (PD) modeling for loans across their full lifecycle often ignores recurrent default events, leading to biased risk estimates. Method: This study systematically evaluates recurrent-event Cox variants—Andersen-Gill (AG) and Prentice-Williams-Peterson (PWP)—against the standard time-to-first-default (TFD) model, using South African mortgage data. We propose a time-varying ROC-based evaluation framework and construct, for the first time, portfolio-level term structures of default risk. Results: In low-recurrence settings, TFD and PWP exhibit statistically indistinguishable predictive performance, whereas AG shows inferior fit. Consequently, TFD can be safely adopted as a parsimonious, computationally efficient, and accurate alternative. This work provides empirical evidence and methodological guidance for PD modeling in sparse recurrent-event contexts under IFRS 9.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Calibration & Uncertainty Quantification
• Natural Language Processing: Discourse, Pragmatics & Argument Mining

Application Category

• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Web Mining and Content Analysis: Models for Web evolution

Abstract

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. Using South African mortgage data, we explore both the Andersen-Gill (AG) and the Prentice-Williams-Peterson (PWP) spell-time models. These models are compared against a baseline that deliberately ignores recurrent events, called the time to first default (TFD) model. Models are evaluated using Harrell's c-statistic, adjusted Cox-Sell residuals, and a novel extension of time-dependent receiver operating characteristic (ROC) 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 at each point of the average loan's lifetime. While the TFD- and PWP-models do not differ significantly across all diagnostics, the AG-model underperformed expectations. Depending on the prevalence of recurrent defaults, one may therefore safely ignore them when estimating lifetime default risk. Accordingly, our work enhances the current practice of using Cox-modelling in producing timeous and accurate PD-estimates under IFRS 9.

Problem

• Modeling lifetime default risk with recurrent events
• Comparing Cox-model subtypes for accurate PD-estimates
• Evaluating models using advanced statistical diagnostics

Innovation

• Uses recurrent event Cox-regression models
• Compares AG and PWP spell-time models
• Applies novel time-dependent ROC analysis