A Practical Approach to Time to Default Forecasting: Stochastic Parametric Modelling with Macroeconomic Variables and Unobserved Consumer Heterogeneity

Abstract

Survival analysis is a competitive alternative to logistic regression when predicting default events but its complexity makes it unfeasible for practitioners. We apply the stochastic parametric Time to Event method to build two models as alternatives to the Cox regression model. Residential mortgage data were used to illustrate performance. Monthly defaults and time varying covariates like Unemployment and Home Price Index are model inputs. Macroeconomic factors are incorporated into the hazard rate function. Forecast accuracy for out-of-time period is acceptable. According to Bellotti ‘any credit risk model with macroeconomic variables can’t be expected to capture the direct reason for default like a loss of job, negative equity or a sudden personal crisis such as sickness or divorce’. To find an approximate solution to this problem, a latent class Weibull model was used, assuming two segments of obligors. We suggest relatively small consumer segment with default hazard increasing over time and relatively large segment with decreasing default hazard. The models can be considered as a simplified aggregate level survival analysis with flexible parameterization. The stochastic parametric Time to Event model has several advantages when comparing with Cox regression and can also be used by practitioners to forecast Time to delinquency, Time to prepayment and Time to recovery.