Survival models for credit risks with time-varying coefficients

Single event survival models predict the probability that an event will occur in the next period of time, given that the event has not happened before. In the context of credit risk, where one may wish to predict the probability of default on a loan account, such models have advantages over cross sectional models, for example they allow the incorporation of time varying factors which may be specific to an account or represent systemic factors. The literature shows that the parameters of such models changed from those before the financial crisis of 2008 to different values after the crisis. In this paper we make two contributions. First we parameterise discrete time survival models of credit card default using B-splines to represent the baseline relationship. These allow a far more flexible specification of the baseline hazard than has been adopted in the literature to date. This baseline relationship is crucial in discrete time survival models and typically has to be specified ex-ante. Second, we allow the estimates of the parameters of the hazard function to themselves be a function of duration time. This allows the relationship between covariates and the hazard to change over time, and to do so in a way that is predictable. Using a large sample of credit card accounts we find that these specifications enhance the predictive accuracy of hazard models over specifications which adopt the type of baseline specification in the current literature and which assume constant parameters.