This paper considers the problem of measuring the credit risk in portfolios of loans, bonds, and other instruments subject to possible default. One such performance measure of interest is the probability that the portfolio incurs large losses over a fixed time horizon. To capture the extremal dependence among obligors, we study a multi-factor model with a normal mixture copula that allows the multivariate defaults to have an asymmetric distribution. Due to the amount of the portfolio, the heterogeneous effect of obligors, and the phenomena that default events are rare and mutually dependent, it is difficult to calculate portfolio credit risk either by means of direct analysis or crude Monte Carlo simulation. That motivates this study on efficient simulation. To this end, we first propose a general account of an importance sampling algorithm based on a two-parameter exponential embedding. Note that this innovative tilting device is more suitable for the multivariate normal mixture model and is of independent interest. Next, by utilizing a fast computational method for how the rare event occurs and the proposed importance sampling method, we provide an efficient simulation algorithm to estimate the probability that the portfolio incurs large losses under the normal mixture copula. Here our proposed simulation device is based on importance sampling for a joint probability other than the conditional probability used in previous studies. Theoretical investigations and simulation studies are given to illustrate the method.
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