Abstract
Motivated from credit risk modeling, this paper extends the twodimensional first passage time problem studied by Zhou (2001) to any finite dimension by means of Monte Carlo simulation. We provide an importance sampling method to estimate the joint default probability, and apply the large deviation principle to prove that the proposed importance sampling is asymptotically optimal. Our result is an alternative to the interacting particle systems proposed by Carmona, Fouque, and Vestal (2009).