  We consider the problem of accurately measuring the credit risk of a
portfolio consisting of loss exposures such as loans, bonds and other financial
assets. We are particularly interested in the probability of large portfolio
losses. We describe the popular models in the credit risk framework including
factor models and copula models. To this end, we revisit the most efficient
probability estimation algorithms within current copula credit risk literature,
namely importance sampling. We illustrate the workings and developments of
these algorithms for large portfolio loss probability estimation and quantile
estimation. We then propose a modification to the dynamic splitting method
which allows application to the credit risk models described. Our proposed
algorithm for the unbiased estimation of rare-event probabilities, exploits the
quasi-monotonic property of functions to embed a static simulation problem
within a time-dependent Markov process. A study of our proposed algorithm is
then conducted through numerical experiments with its performance benchmarked
against current popular importance sampling algorithms.
