  The standard intensity-based approach for modeling defaults is generalized by
making the deterministic term structure of the survival probability stochastic
via a common jump process. The survival copula of the vector of default times
is derived and it is shown to be explicit and of the functional form as dealt
with in the work of Sibuya. Besides the parameters of the jump process, the
marginal survival functions of the default times appear in the copula. Sibuya
copulas therefore allow for functional parameters and asymmetries. Due to the
jump process in the construction, they allow for a singular component.
Depending on the parameters, they may also be extreme-value copulas or
Levy-frailty copulas. Further, Sibuya copulas are easy to sample in any
dimension. Properties of Sibuya copulas including positive lower orthant
dependence, tail dependence, and extremal dependence are investigated. An
application to pricing first-to-default contracts is outlined and further
generalizations of this copula class are addressed.
