Models for default rates in credit portfolios

Abstract

The default rate is a measure widely used in credit risk management. This reflects the probability that obligors will default on their credit obligations over a specified time horizon. Our aim is to formulate statistical models that can describe the default rate dynamics and to forecast future default tendencies of credit portfolios. Auto-regressive (AR) models and various extended forms of AR models are used for this purpose. The extended AR models incorporate observed exogenous factors (such as economic variables) as well as unobserved or latent components. A restricted multivariate vector auto-regressive (VAR) model is also explored in this context. Monthly default rates data of a mortgage loans portfolio was obtained and used to illustrate the statistical methodology required to fit these models. Since default rates often have very small values and highly skewed distributions, probit and logistic transformations of the rates were necessary before model fitting could be done. For this data, it was found that using only 1 auto-regressive term was sufficient. However, the inclusion of economic variables (e.g. CPIX) and the use of multivariate models were not completely satisfactory and therefore AR{\) models extended with unobserved components were developed and applied to the data. These unobserved components were assumed to have AR{\) dynamics of their own and this made the use of standard software packages impossible when fitting these models by maximum likelihood estimation methods. For this purpose and also for forecasting, methods were developed based on the Kalman filter and the Expectation-Maximization (EM)-algorithm. This formed the main contribution of this work.