Dynamic Multi-Factor Credit Portfolio Model for

This paper derives new analytical solutions for limiting loss distributions for portfolio of homogeneous loans based on multivariate skew normal and multivariate skew t distributions. Both the static and dynamic models are tested using U.S. sector charge-off ratios over the period Q1:1985 to Q2:2010. Our analytical solutions greatly simplified the static model estimations. The dynamic model allows the factors to have time series structures, which are estimated using particle filtering and Markov Chain Monte Carlo method. Our skew normal model and analytical solution can be seen as a two-factor extension to Vasicek's single factor model which is core to Basel II determination of regulatory capital for banks. The static and dynamic risk estimates correspond to the `through the cycle' and the `point in time' approaches to risk management.