Better Confidence Intervals for Importance Sampling

It is well known that for highly skewed distributions the standard
method of using the t statistic for the confidence interval of the
mean does not give robust results. This is an important problem for
importance sampling (IS) as its final distribution is often skewed due
to a heavy tailed weight distribution. In this paper, we first explain
Hall's transformation and its variants to correct the confidence
interval of the mean and then evaluate the performance of these
methods for two numerical examples from finance which have closed-form
solutions. Finally, we assess the performance of these methods for
credit risk examples. Our numerical results suggest that Hall's
transformation or one of its variants can be safely used in correcting
the two-sided confidence intervals of financial simulations.