Tails of Credit Default Portfolios

We derive analytic expressions for the tail behavior of credit
losses in a large homogeneous credit default portfolio. Our model
is an extended CreditMetrics model; i.e. it is a one-factor model
with a multiplicative shock-variable. We show that the first order
tail behavior is robust with respect to this shock-variable. In a
simulation study we compare different models for the latent
variables. We fix default probability and correlation of the latent
variables and the first order tail behavior of the limiting credit
losses in all modelsand observe a completely different tail
behavior leading to very different VaR estimates. For three
portfolios of different credit quality we suggest a pragmatic model
selection procedure and compare the fit with that of the
beta-model.