Better confidence intervals for importance sampling

Abstract

It is well known that for highly skewed distributions the standard method of using the t statistic for the confidence interval for 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. On the poster, we first explain the Hall's transformation to correct the confidence interval of the mean and then evaluate the performance of this method for two numerical examples from finance, which have closed form solutions. Finally, we assess the performance of this method for the credit risk examples. Our numerical results suggest that Hall's transformation can be safely used in correcting the confidence intervals of financial simulations.