Exploring different subtypes of recurrent event Cox-regression models in modelling lifetime default risk: A tutorial
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| author | Botha, Arno Verster, Tanja Scheepers, Bernard |
| author_facet | Botha, Arno Verster, Tanja Scheepers, Bernard |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_01044 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exploring different subtypes of recurrent event Cox-regression models in modelling lifetime default risk: A tutorial Botha, Arno Verster, Tanja Scheepers, Bernard Risk Management Statistical Finance Applications 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. |
| title | Exploring different subtypes of recurrent event Cox-regression models in modelling lifetime default risk: A tutorial |
| topic | Risk Management Statistical Finance Applications |
| url | https://arxiv.org/abs/2505.01044 |