Modeling Time to Default on a Personal Loan Portfolio in Presence of Disproportionate Hazard Rates

In this paper we consider a parametric Weibull mixture cure model for modeling time to default on a personal loan portfolio in presence of disproportionate hazard rate. The main contribution of this paper is to evidence that mixture cure models are appropriate for non proportional sceneries, which has not been claimed in recent articles that brings survival analysis approach for credit scoring modeling. A straight comparison with well known proportional hazard mixture cure model presented in Peng and Dear (2000), provides evidence that risk measurements derived from this framework can be greatly affected if required proportional conditions are not satisfied. In fact, taking into account presence of covariates, if covariates levels do not have proportional hazards rate over time, adjustment with models that assume proportional hazard rates will not be appropriate, and then, erroneous measurements may be derived, i.e., under or overestimate expected losses of a portfolio can be observed. Our approach can be seen as a complement to modeling framework presented in Tong et al. (2012) for credit scoring purposes, which require a proportional hazard structure. A credit data from a Brazilian commercial bank illustrates the procedure.