A new robust importance-sampling method for measuring value-at-risk and expected shortfall allocations for credit portfolios

ABSTRACT We propose a new importance-sampling technique for value-at-risk estimation and expected shortfall allocation for a credit portfolio. A key element of any model of portfolio credit risk is a mechanism for capturing dependence among obligors. This paper is mainly focused on the multifactor normal copula model. However, we also show how the proposed method can be applied to a t-copulabased credit-loss model. Our method uses a combination of mean shifting and exponential twisting for the systematic and the specific factors, respectively, and it differs from previously proposed methods in that the mean shift is determined using Markov chain Monte Carlo sampling. We show with examples that the Markov chain Monte Carlo method works satisfactorily for a wide variety of correlation structures. Moreover, our method is shown to work well even when the normal copula is replaced by a t-copula. 1