  Computation of extreme quantiles and tail-based risk measures using standard
Monte Carlo simulation can be inefficient. A method to speed up computations is
provided by importance sampling. We show that importance sampling algorithms,
designed for efficient tail probability estimation, can significantly improve
Monte Carlo estimators of tail-based risk measures. In the heavy-tailed
setting, when the random variable of interest has a regularly varying
distribution, we provide sufficient conditions for the asymptotic relative
error of importance sampling estimators of risk measures, such as Value-at-Risk
and expected shortfall, to be small. The results are illustrated by some
numerical examples.
