Multihorizon discrete time survival models

The new accounting standards of CECL for the US and IFRS 9 elsewhere require predictions of lifetime losses for loans. The use of roll rates, state transition and "vintage" models has been proposed and indeed are used by practitioners. The first two methods are relatively more accurate for predictions of up to one year, because they include lagged delinquency as a predictor, whereas "vintage" models are more accurate for predictions for longer periods, but not short periods because they omit delinquency as a predictor variable. In this paper we propose the use of survival models that include lagged delinquency as a covariate and show, using a large sample of 30 year mortgages, that the proposed method is more accurate than any of the other three methods for both short-term and long-term predictions of the probability of delinquency. We experiment extensively to find the appropriate lagging structure for the delinquency term. The results provide a new method to make lifetime loss predictions, as required by CECL and IFRS 9 Stage 2.