Forecasting Forward Defaults with the Discrete-Time Hazard Model

For predicting forward default probabilities of firms, the discrete‐time forward hazard model (DFHM) is proposed. We derive maximum likelihood estimates for the parameters in DFHM. To improve its predictive power in practice, we also consider an extension of DFHM by replacing its constant coefficients of firm‐specific predictors with smooth functions of macroeconomic variables. The resulting model is called the discrete‐time varying‐coefficient forward hazard model (DVFHM). Through local maximum likelihood analysis, DVFHM is shown to be a reliable and flexible model for forward default prediction. We use real panel datasets to illustrate these two models. Using an expanding rolling window approach, our empirical results confirm that DVFHM has better and more robust out‐of‐sample performance on forward default prediction than DFHM, in the sense of yielding more accurate predicted numbers of defaults and predicted survival times. Thus DVFHM is a useful alternative for studying forward default losses in portfolios.