Testing Observable and Latent Risk Factor Models for Systematic Credit Risk on a Large Loan Level Data Set of Residential Mortgages

This paper compares the performance of two models for probability of default of residential mortgages, namely a two-step logistic regression model with observable systematic risk factor and a mixed-measurement observation driven generalized autoregressive score (GAS) model. The data set is of residential mortgages set available by the Federal National Mortgage Association. The comparison of the models is realized in two different settings, namely a setting where the data set covers a complete economic cycle and a setting where the data set only covers parts of the economic cycle. Specifically, this paper focuses on the implications of restrictions in the length of loan level observations for the estimation of the two models. This is specially of interest since the length of loan level data sets might not fully cover economic cycles. Thus, resulting in biased model estimates. The results obtained in this paper indicate that the length of the data set plays a significant role defining the maximum likelihood estimates of both models. Furthermore, it is shown that the mix-measurement observation driven GAS model provides a very flexible framework capable of incorporating all futures of the two-step logit model with observable risk factor. By comparing the out-of-sample forecasting performance of both models it is shown that the GAS model can perform significantly better in periods of economic distress. This paper provides a comprehensive and detailed description of how the mix-measurement observation driven GAS model can be applied to estimate the probability of default of residential mortgages. Thus, providing financial institutions with an additional and rather accurate tool to estimate regulatory capital of retail portfolios.