Tail Distribution of the Maximum of Correlated Gaussian Random Variables
Tinbergen Institute Discussion Paper 15-132/III
14 Pages Posted: 16 Dec 2015
Date Written: December 11, 2015
Abstract
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.
Keywords: Rare event simulation, Correlated Gaussian, Tail probabilities, Sequential importance sampling
JEL Classification: C61, C63
Suggested Citation: Suggested Citation