64th ISI World Statistics Congress - Ottawa, Canada

64th ISI World Statistics Congress - Ottawa, Canada

Modelling the resolution time of defaulted loans using cure models with a frailty component


Marius Smuts



64th ISI World Statistics Congress - Ottawa, Canada

Format: CPS Abstract

Keywords: survival analysis


In recent years, statistical models within the credit risk environment have become increasingly popular. Initially, the focus was on the assessment of a counterparty's creditworthiness (i.e. default risk), however the modelling of the recovery process and outcome after default is receiving more and more attention. Two main outcomes, or resolutions, after default are possible: the outstanding amount is fully recovered, or the loan is written off. There exist several obligor and loan specific factors that may influence a loan's probability of being written off. Some of these factors are observable and can be included in a model as covariates, but some factors, for example an individual's level of discretionary expenditure and undisclosed debt, are latent. There also exists a proportion of defaulted loans for which the outstanding amounts will be fully recovered and is therefore not exposed to write-off. In our context these loans can be considered "cured". The time to write-off or full recovery may, in addition to latent competing risks, also be influenced by common, unobservable drivers, such as the state of the economy; we therefore propose to use a promotion time cure model and include a frailty parameter to control for heterogeneity. We evaluate the performance of the model via a small Monte Carlo study and also apply it to a real world banking data set, where it is found that the new model outperforms the more traditional models.