Assessment of Mortgage Default Risk via Bayesian State Space Models

Managing risk at the aggregate level is crucial for banks and financial
institutions as required by the Basel II framework. In modeling mortgage
default risk at the aggregate level, issues such identifying the dynamic
behavior of default rate as well as the effect of macroeconomic variables
on default risk are of concern to both practitioners and researchers. In
addressing these issues, we propose discrete time Bayesian state space
models with Poisson observations and a stochastic default rate. In doing so
we discuss parameter updating and estimation using Markov chain Monte Carlo
methods. In assessing the dynamic nature of the mortgage default rate, we
compare the forecasting performance of the proposed models with a Bayesian
Poisson regression model used as a benchmark. We illustrate the use of the
proposed models using actual U.S. residential mortgage data and discuss
insights gained from Bayesian analysis. Furthermore, we discuss
multivariate extensions of the proposed model.