  We propose a novel credit default model that takes into account the impact of
macroeconomic information and contagion effect on the defaults of obligors. We
use a set-valued Markov chain to model the default process, which is the set of
all defaulted obligors in the group. We obtain analytic characterizations for
the default process, and use them to derive pricing formulas in explicit forms
for synthetic collateralized debt obligations (CDOs). Furthermore, we use
market data to calibrate the model and conduct numerical studies on the tranche
spreads of CDOs. We find evidence to support that systematic default risk
coupled with default contagion could have the leading component of the total
default risk.
