Importance sampling for a mixed Poisson model of portfolio credit risk

Simulation is widely used to estimate losses due to default and other credit events in financial portfolios. The challenge in doing this efficiently results from (i) rare-event aspects of large losses and (ii) complex dependence between defaults of multiple obligors. We discuss importance sampling techniques to address this problem in two portfolio credit risk models developed in the financial industry, with particular emphasis on a mixed Poisson model. We give conditions for asymptotic optimality of the estimators as the portfolio size grows.