  The classical reduced-form and filtration expansion framework in credit risk
is extended to the case of multiple, non-ordered defaults, assuming that
conditional densities of the default times exist. Intensities and pricing
formulas are derived, revealing how information driven default contagion arises
in these models. We then analyze the impact of ordering the default times
before expanding the filtration. While not important for pricing, the effect is
significant in the context of risk management, and becomes even more pronounced
for highly correlated and asymmetrically distributed defaults. Finally, we
provide a general scheme for constructing and simulating the default times,
given that a model for the conditional densities has been chosen.
