Modeling multi-period corporate default probability when hazard ratios decay

ABSTRACT A number of researchers have used the Cox proportional hazards model to estimate multiperiod corporate default probabilities. By construction, models estimated in this manner have hazard ratios that are constant over time. We present evidence, drawn from historical data, indicating that empirical hazard ratios, in fact, exhibit pronounced decay over time, contrary to the assumptions of the Cox proportional hazards model. We provide a possible explanation for this phenomenon, in terms of the evolution, posited by other authors, of the explanatory variables. We propose a hazard rate model with timevarying coefficients, which incorporates the decaying hazard ratio property. Our model outperforms the standard Cox proportional hazards model on an out-ofsample/ time experiment.