Importance sampling for portfolio credit risk

The main challenge in modern credit risk management is to construct the loss distribution at the portfolio level. Monte Carlo simulation is a widely used computational tool to get this distribution. It can be rather slow since estimating the loss distribution is basically a rare-event problem. This motivates research to accelerate simulation by variance reduction techniques.; Importance sampling (IS) is a potentially attractive variance reduction technique in estimating the loss distribution since it is especially effective in the rare-event situation. Yet the application of IS is complicated by the mechanism to model dependence between obligors, and capturing this dependence is essential to a portfolio view of credit risk which is an important feature of modern credit risk management.; This dissertation studies the dependence structures in two portfolio credit risk models. The first one is the widely used normal copula model and the second one is the mixed Poisson model. We propose an IS procedure to construct the portfolio loss distribution for both models. The procedure has two parts: one applies IS conditional on a set of common factors affecting multiple obligors, the other applies IS to the factors themselves. The relative importance of the two parts of the procedure is determined by the strength of the dependence between obligors. We provide both theoretical and numerical support for the method.