Joint survival probability via truncated invariant copula

• We have studied an issue of dependence structure between default intensities.
• We use a multivariate shot noise intensity process, where jumps occur simultaneously and their sizes are correlated.
• We obtain the joint survival probability of the integrated intensities by using a copula.
• We apply our theoretical result to pricing basket default swap spread.

Given an intensity-based credit risk model, this paper studies dependence structure between default intensities. To model this structure, we use a multivariate shot noise intensity process, where jumps occur simultaneously and their sizes are correlated. Through very lengthy algebra, we obtain explicitly the joint survival probability of the integrated intensities by using the truncated invariant Farlie–Gumbel–Morgenstern copula with exponential marginal distributions. We also apply our theoretical result to pricing basket default swap spreads. This result can provide a useful guide for credit risk management.