Monte Carlo for large credit portfolios with potentially high correlations

In this paper we develop efficient Monte Carlo methods for large credit portfolios. We assume the default indicators admit a Gaussian copula. Therefore, we are able to embed the default correlations into a continuous Gaussian random field, which is capable of incorporating an infinite size portfolio and potentially highly correlated defaults. We are particularly interested in estimating the expectations, such as the expected number of defaults given that there is at least one default and the expected loss given at least one default. All these quantities turn out to be closely related to the geometric structure of the random field. We will heavily employ random field techniques to construct importance sampling based estimators and provide rigorous efficiency analysis.