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Bayesian Inference for Generalized Linear Mixed Models of Portfolio Credit Risk

by Alexander J. McNeil of ETH Zürich, and
Jonathan Wendin of ETH Zürich

October 5, 2005

Abstract: 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-of-the-economy suggests the presence of a residual, cyclical, latent component in the systematic risk.

JEL Classification: G31, G11, C15.

Keywords: Credit risk, Generalized linear mixed model, State space model, Bayesian inference.

Published in: Journal of Empirical Finance, Vol. 14, No. 2, (March 2007), pp. 131-149.

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