We model 1981–2002 annual US default frequencies for a panel of firms in different rating and age classes. The data is decomposed into a systematic and firm-specific risk component, where the systematic component reflects the general economic conditions and default climate. We have to cope with (i) the shared exposure of each age cohort and rating class to the same systematic risk factor; (ii) strongly non-Gaussian features of the individual time series; (iii) possible dynamics of an unobserved common risk factor; (iv) changing default probabilities over the age of the rating, and (v) missing observations. We propose a non-Gaussian multivariate state space model that deals with all of this issues simultaneously. The model is estimated using importance sampling techniques that have been modified in a multivariate setting. This multivariate approach has significant advantages in terms of parameter stability and convergence of the importance sampler.
credit risk multivariate unobserved component models importance sampling non-Gaussian state space models