  In this paper we propose a simple and efficient method to compute the ordered
default time distributions in both the homogeneous case and the two-group
heterogeneous case under the interacting intensity default contagion model. We
give the analytical expressions for the ordered default time distributions with
recursive formulas for the coefficients, which makes the calculation fast and
efficient in finding rates of basket CDSs. In the homogeneous case, we explore
the ordered default time in limiting case and further include the exponential
decay and the multistate stochastic intensity process. The numerical study
indicates that, in the valuation of the swap rates and their sensitivities with
respect to underlying parameters, our proposed model outperforms the Monte
Carlo method.
