Tail Distribution of the Maximum of Correlated Gaussian Random Variables

Tinbergen Institute Discussion Paper 15-132/III

14 Pages Posted: 16 Dec 2015

See all articles by Zdravko Botev

Zdravko Botev

University of New South Wales (UNSW)

Michel Mandjes

University of Amsterdam

Ad Ridder

VU University Amsterdam - Department of Econometrics and Operations Research; Tinbergen Institute

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

Botev, Zdravko and Mandjes, Michel and Ridder, Ad, Tail Distribution of the Maximum of Correlated Gaussian Random Variables (December 11, 2015). Tinbergen Institute Discussion Paper 15-132/III, Available at SSRN: https://ssrn.com/abstract=2703769 or http://dx.doi.org/10.2139/ssrn.2703769

Zdravko Botev (Contact Author)

University of New South Wales (UNSW) ( email )

Kensington
High St
Sydney, NSW 2052
Australia

Michel Mandjes

University of Amsterdam ( email )

Spui 21
Amsterdam, 1018 WB
Netherlands

Ad Ridder

VU University Amsterdam - Department of Econometrics and Operations Research ( email )

De Boelelaan 1105
1081 HV Amsterdam
Netherlands

HOME PAGE: http://personal.vu.nl/a.a.n.ridder/

Tinbergen Institute ( email )

Gustav Mahlerplein 117
Amsterdam, 1082 MS
Netherlands

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