This thesis develops Bayesian models to explain credit default and migration risk.
Credit risk models used in practice are based on an assumption of conditionally independent
events given a realization of systematic risk factors. The systematic risk can
be modelled with both observed and unobserved factors.
On the one hand we consider generalised linear mixed models (GLMMs) for default
count data where random e ects account for unobserved factor risk. On the other
hand we consider survival models with shared frailties to model unobserved factors in
time-to-default and time-to-rating-transition data. The latter models are developed
in the Anderson-Gill counting process framework for the Cox proportional hazards
model to allow multiple events and time-dependent covariates.
Using Standard and Poor's data on default and rating transitions we control for
observed macroeconomic factors in the xed e ect parts of the models. We allow the
latent factors to have autoregressive time series structure.
The results from both kinds of model show clear evidence of heterogeneity between
industry sectors/countries and time period suggesting that di erent latent factor effects
are present in di erent sectors. This is an important message that should be
accounted for in risk analyses.
We implement Bayesian inference for all our models and use the MCMC approach
(Gibbs sampling). We show some tractable model formulations that capture the
main sources and implement Bayesian model choice procedures to select the most
explanatory models.
There are couple of contributions in this thesis: First, this is an analysis of industry
e ects on default and migration rates using vector-valued random e ects in default
count models and vector-valued dynamic frailties in time-to-event/survival models.
While this has been done before in models for default counts (McNeil-Wendin) it is
quite novel for time-to-event models. Koopman, Lucas and Schwaab (2012) which has
some similarities but the estimation is by Monte Carlo maximum likelihood, not by
Bayesian methods. Second, estimation of rating transition model with shared dynamic
frailties for di erent industry sectors and macroeconomic covariates using Bayesian
techniques (MCMC). This is a new model which is based on a simpler model used in
medical statistics (Manda & Mayer(2005)) that has been adapted and extended for
the credit risk application. We show how to estimate the new model using a Bayesian
approach. Finally, we use the model to compute point-in-time dynamic estimates of
rating transition probabilities for di erent industry sectors and forecast these into the
future, while taking into account macroeconomic factors. This can be very useful for
risk management applications and economic scenario generation
