Modelling the Time to Write-Off of Non-Performing Loans Using a Promotion Time Cure Model with Parametric Frailty

Janette Larney (), James Samuel Allison, Gerrit Lodewicus Grobler and Marius Smuts
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Janette Larney: Centre for Business Mathematics and Informatics, North-West University, Potchefstroom 2531, South Africa
James Samuel Allison: School of Mathematical and Statistical Sciences, North-West University, Potchefstroom 2531, South Africa
Gerrit Lodewicus Grobler: School of Mathematical and Statistical Sciences, North-West University, Potchefstroom 2531, South Africa
Marius Smuts: School of Mathematical and Statistical Sciences, North-West University, Potchefstroom 2531, South Africa

Mathematics, 2023, vol. 11, issue 10, 1-17

Abstract: Modelling the outcome after loan default is receiving increasing attention, and survival analysis is particularly suitable for this purpose due to the likely presence of censoring in the data. In this study, we suggest that the time to loan write-off may be influenced by latent competing risks, as well as by common, unobservable drivers, such as the state of the economy. We therefore expand on the promotion time cure model and include a parametric frailty parameter to account for common, unobservable factors and for possible observable covariates not included in the model. We opt for a parametric model due to its interpretability and analytical tractability, which are desirable properties in bank risk management. Both a gamma and inverse Gaussian frailty parameter are considered for the univariate case, and we also consider a shared frailty model. A Monte Carlo study demonstrates that the parameter estimation of the models is reliable, after which they are fitted to a real-world dataset in respect of large corporate loans in the US. The results show that a more flexible hazard function is possible by including a frailty parameter. Furthermore, the shared frailty model shows potential to capture dependence in write-off times within industry groups.

Keywords: survival analysis; write-off time; loan recovery; promotion time cure model; parametric frailty; shared frailty (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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