STOCHASTIC AND COPULA MODELS FOR CREDIT DERIVATIVES

We prove results relating to the exit time of a stochastic process from a region in N-dimensional space. We compute certain stochastic integrals involving the exit time. Taking a Gaussian copula model for the hitting time behavior We derive explicit formulas for CDO tranche sensitivity to parameter variations and prove results concerning the qualitative behavior of such tranche sensitivities as well as the large-N behavior for a homogeneous portfolio governed by the one-factor Gaussian copula. A Poisson-mixture model is also investigated in a similar vein. Relevant simulations are presented.