Bayesian inference for generalized linear mixed models of portfolio credit risk

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 historical 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 and Poor's data on U.S. 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.

[1]  Matthew Kurbat,et al.  Methodology for Testing the Level of the EDF Credit Measure , 2002 .

[2]  Alan E. Gelfand,et al.  Model Determination using sampling-based methods , 1996 .

[3]  Christian P. Robert,et al.  Monte Carlo Statistical Methods , 2005, Springer Texts in Statistics.

[4]  Christian Gourieroux,et al.  Financial Valuation and Risk Management Working Paper No . 294 Stochastic Migration Models with Application to Corporate Risk , 2006 .

[5]  P. McCullagh,et al.  Generalized Linear Models, 2nd Edn. , 1990 .

[6]  David G. Clayton,et al.  Generalized linear mixed models , 1996 .

[7]  Christian Gourieroux,et al.  Simulation-based econometric methods , 1996 .

[8]  P. McCullagh,et al.  Generalized Linear Models , 1992 .

[9]  Estimating Default Correlations from Short Panels of Credit Rating Performance Data , 2003 .

[10]  Walter R. Gilks,et al.  Full conditional distributions , 1995 .

[11]  Richard A. Davis,et al.  Time Series: Theory and Methods (2nd ed.). , 1992 .

[12]  R. C. Merton,et al.  On the Pricing of Corporate Debt: The Risk Structure of Interest Rates , 1974, World Scientific Reference on Contingent Claims Analysis in Corporate Finance.

[13]  W. Perraudin,et al.  Stability of ratings transitions , 2001 .

[14]  Sylvia Richardson,et al.  Markov Chain Monte Carlo in Practice , 1997 .

[15]  Siem Jan Koopman,et al.  A Non-Gaussian Panel Time Series Model for Estimating and Decomposing Default Risk , 2003 .

[16]  T. C. Wilson,et al.  Portfolio Credit Risk , 1998 .

[17]  Daniel Egloff,et al.  A Simple Model of Credit Contagion , 2004 .

[18]  C. McCulloch.  Maximum Likelihood Algorithms for Generalized Linear Mixed Models , 1997 .

[19]  H. Joe.  Multivariate models and dependence concepts , 1998 .

[20]  Dawn Hunter.  Dependent defaults in models of portfolio credit risk , 2003 .

[21]  John A. Nelder,et al.  Generalized linear models. 2nd ed. , 1993 .

[22]  S. E. Hills,et al.  Illustration of Bayesian Inference in Normal Data Models Using Gibbs Sampling , 1990 .

[23]  Richard A. Davis,et al.  Time Series: Theory and Methods , 2013 .

[24]  Eric R. Ziegel,et al.  Multivariate Statistical Modelling Based on Generalized Linear Models , 2002, Technometrics.

[25]  Mark H. A. Davis,et al.  A Hidden Markov Model of Default Interaction , 2003 .

[26]  Til Schuermann,et al.  Ratings Migration and the Business Cycle, with Application to Credit Portfolio Stress Testing , 2000 .

[27]  Jose A. Lopez.  The Empirical Relationship between Average Asset Correlation, Firm Probability of Default and Asset Size , 2002 .

[28]  N. Breslow,et al.  Approximate inference in generalized linear mixed models , 1993 .

[29]  L. Corrado.  Generalized Latent Variable Modeling: Multilevel, Longitudinal, and Structural Equation Models , 2005 .

[30]  田中 豊.  Multivariate Statistical Modelling Based on Generalized Linear Models/Ludwig Fahrmeir,Gerhard Tutz(1994) , 1995 .

[31]  Eric R. Ziegel,et al.  Generalized Linear Models , 2002, Technometrics.

[32]  Jonathan Wendin.  Bayesian methods in portfolio credit risk management , 2006 .

[33]  Göran Broström,et al.  Generalized linear models with random intercepts , 2003 .

[34]  Martin Crowder,et al.  Analysis of default data using hidden Markov models , 2005 .

[35]  Daniel Roesch,et al.  An Empirical Comparison of Default Risk Forecasts from Alternative Credit Rating Philosophies , 2004 .

[36]  S. Koopman,et al.  Empirical credit cycles and capital buffer formation , 2005 .

[37]  W. Perraudin,et al.  Stability of ratings transitions , 2001 .