Importance Sampling for Portfolio Credit Risk
Paul Glasserman
Graduate School of Business
Columbia University
Abstract
The distribution of losses due to defaults in large portfolios
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, particularly in the
industry-standard Gaussian copula model. 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 and give conditions for asymptotic
optimality. We also develop IS methods for conditional
expectations used to measure marginal risk contributions.
This is based on joint work with Jingyi Li.