Managing risk at the aggregate level is crucial for banks and financial
institutions as required by the Basel III framework. In this paper, we
introduce discrete time Bayesian state space models with Poisson measurements
to model aggregate mortgage default rate. We discuss parameter updating,
filtering, smoothing, forecasting and estimation using Markov chain Monte Carlo
methods. In addition, we investigate the dynamic behavior of the default rate
and the effects of macroeconomic variables. We illustrate the use of the
proposed models using actual U.S. residential mortgage data and discuss
insights gained from Bayesian analysis.
