Monte Carlo Methods for Portfolio Credit Risk

The distribution of losses due to defaults in a large portfolio is often computed using Monte Carlo simulation and can therefore be time consuming, particularly when precise estimates are required for small probabilities of large losses. Importance sampling (IS) is a general technique for improving the performance of Monte Carlo methods in estimating rare-event probabilities. However, the application of IS to credit risk is complicated by the mechanisms commonly used to specify the dependence between default events. We present a two-step approach to IS for credit losses that takes advantage of the "factor" structure often used in credit models: we apply IS conditional on the factors and then apply IS to the factors themselves. We analyze the effectiveness of the method through asymptotics in the size of portfolio. This is based on joint work with Jingyi Li.