A0187
Title: Towards modeling lifetime default risk: Exploring different subtypes of recurrent event Cox-regression models
Authors: Tanja Verster - North-West University (South Africa) [presenting]
Arno Botha - North-West University (South Africa)
Bernard Scheepers - North-West University (South Africa)
Abstract: In the pursuit of modeling 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, a few subtypes of Cox models that can incorporate recurrent default events are investigated. Using South African mortgage data, both the Andersen-Gill (AG) and the Prentice-Williams-Peterson (PWP) spell-time models are explored. 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, it is demonstrated 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, the current practice of using Cox-modeling is enhanced in producing timeous and accurate PD-estimates under IFRS 9.
