# 15-132/III (2015-12-15)

Author(s)
Zdravko Botev, The University of New South Wales, Sydney, Australia; Michel Mandjes, University of Amsterdam, the Netherlands; Ad Ridder, VU University Amsterdam, the Netherlands
Keywords:
Rare event simulation, Correlated Gaussian, Tail probabilities, Sequential importance sampling
JEL codes:
C61, C63

In this article we consider the efficient estimation of the tail distribution of the maximum of correlated normal random variables. We show that the currently
recommended Monte Carlo estimator has difficulties in quantifying its precision, because its sample variance estimator is an inefficient estimator of the true variance.
We propose a simple remedy: to still use this estimator, but to rely on an alternative quantification of its precision. In addition to this we also consider a completely new sequential importance sampling estimator of the desired tail probability. Numerical experiments suggest that the sequential importance sampling estimator can be
significantly more efficient than its competitor.