Joint models for longitudinal and discrete survival data in credit scoring

Keywords OR in banking; Bayesian joint models; Discrete time; Autoregressive process Highlights * This paper proposes a joint model with autoregressive terms in the longitudinal outcome. * A discrete time framework is applied to credit scoring. * We analyse 10,399 mortgage loans originated in the US. * Our proposal increases the discrimination performance of traditional survival models. Abstract The inclusion of time-varying covariates into survival analysis has led to better predictions of the time to default in behavioural credit scoring models. However, when these time-varying covariates are endogenous, there are two major problems: estimation bias of the survival model and lack of a prediction framework for future values of both the event and the endogenous time-varying covariates. Joint models for longitudinal and survival data is an appropriate framework to model the mutual evolution of the survival time and the endogenous time-varying covariates. To the best of our knowledge, this paper explores for the first time the application of discrete-time joint models to credit scoring. Moreover, we propose a novel extension to the joint model literature by including autoregressive terms in modelling the endogenous time-varying covariates. We present the method via simulations and by applying it to US mortgage loans. The empirical analysis shows, first, that discrete joint models can increase the discrimination performance compared to survival models. Second, when an autoregressive term is included, this performance can be further improved. Author Affiliation: (a) Business School, University of Edinburgh, United Kingdom (b) School of Mathematics, University of Edinburgh, United Kingdom * Corresponding author. Article History: Received 22 December 2020; Accepted 12 October 2022 Byline: Victor Medina-Olivares [victor.medina@ed.ac.uk] (*,a), Raffaella Calabrese (a), Jonathan Crook (a), Finn Lindgren (b)