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We consider the problem of accurately measuring the credit risk of aportfolio consisting of loss exposures such as loans, bonds and other financialassets. We are particularly interested in the probability of large portfoliolosses. We describe the popular models in the credit risk framework includingfactor models and copula models. To this end, we revisit the most efficientprobability estimation algorithms within current copula credit risk literature,namely importance sampling. We illustrate the workings and developments ofthese algorithms for large portfolio loss probability estimation and quantileestimation. We then propose a modification to the dynamic splitting methodwhich allows application to the credit risk models described. Our proposedalgorithm for the unbiased estimation of rare-event probabilities, exploits thequasi-monotonic property of functions to embed a static simulation problemwithin a time-dependent Markov process. A study of our proposed algorithm isthen conducted through numerical experiments with its performance benchmarkedagainst current popular importance sampling algorithms.

The Dynamic Splitting Method with an application to portfolio credit risk