Dynamic survival models with time varying coefficients for credit risks

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. The literature shows that the parameters of such models changed after compared with before the financial crisis of 2008. But there is also the possibility that the sensitivity of the probability of default, to say behavioural variables, changes over the life of an account.

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. 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.