The aims of this paper are threefold. First we highlight the usefulness of generalized linear mixed models (GLMMs) in the modelling of portfolio credit default risk. The GLMM-setting allows for a flexible specification of the systematic portfolio risk in terms of observed fixed effects and unobserved random effects, in order to explain the phenomena of default dependence and time-inhomogeneity in empirical default data. Second we show that computational Bayesian techniques such as the Gibbs sampler can be successfully applied to fit models with serially correlated random effects, which are special instances of state space models. Third we provide an empirical study using Standard & Poor’s data on US firms. A model incorporating rating category and sector effects and a macroeconomic proxy variable for state-ofthe-economy suggests the presence of a residual, cyclical, latent component in the systematic risk.

The following article develops a simultaneous multi-factor model for defaults and recoveries. Applying this model, risk parameters can be forecast using systematic and idiosyncratic risk factors and their implied correlations. The theoretical framework is accompanied by an empirical analysis in which a negative correlation between defaults and recoveries over the business cycle is observed. In the study, default and recovery rates are modeled by business cycle indicators and the properties of the economic and regulatory capital given these risk drivers are shown.

This paper examines latent risk factors in models for migration risk. We employ the standard statistical framework for ordered categorical variables and induce dependence between migrations by means of latent risk factors. By assuming a Markov process for the dynamics of the latent factors, the model can be interpreted as a state space model. The paper contains an empirical study on quarterly migration data from Standard & Poor’s for the years 1981–2000, in which the ordered logit model with serially correlated latent factors is fitted by computational Bayesian techniques (Gibbs sampling). Apart from highlighting the usefulness of the Gibbs sampler for statistical inference in models of this kind, the survey in particular investigates the issues of rating-specific factor loadings and heterogeneity among industry sectors, with emphasis on their implications in terms of implied asset correlations.

Capital Accord (Basel II), Capital Requirements Directive (CRD), capital structure, business

JEL classification: G21, G28, G33The views expressed in this paper are those of their authors and not necessarily the views of the Financial Stability Institute or the Bank for International Settlements. Copies of publications are available from:

The authors would like to thank Kaveh Navaian at Zürcher Kantonalbank and the anonyms reviewer for their helpful comments and suggestions. The authors would also like to thank A. Bloechlinger, M. Buechler, D. Schenker and J. Syz at Zürcher Kantonalbank for their assistance. We would like to extend