Value‐At‐Risk Bounds with Variance Constraints

37 Pages Posted: 15 Aug 2017

See all articles by Carole Bernard

Carole Bernard

Grenoble Ecole de Management; Vrije Universiteit Brussel (VUB)

Ludger Rüschendorf

University of Freiburg

Steven Vanduffel

Vrije Universiteit Brussel (VUB)

Multiple version iconThere are 2 versions of this paper

Date Written: September 2017

Abstract

We study bounds on the Value‐at‐Risk (VaR) of a portfolio when besides the marginal distributions of the components its variance is also known, a situation that is of considerable interest in risk management. We discuss when the bounds are sharp (attainable) and also point out a new connection between the study of VaR bounds and the convex ordering of aggregate risk. This connection leads to the construction of an algorithm, called Extended Rearrangement Algorithm (ERA), that makes it possible to approximate sharp VaR bounds. We test the stability and the quality of the algorithm in several numerical examples. We apply the results to the case of credit risk portfolio models and verify that adding the variance constraint gives rise to significantly tighter bounds in all situations of interest.

Suggested Citation

Bernard, Carole and Rüschendorf, Ludger and Vanduffel, Steven, Value‐At‐Risk Bounds with Variance Constraints (September 2017). Journal of Risk and Insurance, Vol. 84, Issue 3, pp. 923-959, 2017. Available at SSRN: https://ssrn.com/abstract=3018865 or http://dx.doi.org/10.1111/jori.12108

Carole Bernard (Contact Author)

Grenoble Ecole de Management ( email )

12, rue Pierre Sémard
Grenoble Cedex, 38003
France

Vrije Universiteit Brussel (VUB) ( email )

Pleinlaan 2
http://www.vub.ac.be/
Brussels, 1050
Belgium

Ludger Rüschendorf

University of Freiburg ( email )

Fahnenbergplatz
Freiburg, D-79085
Germany

Steven Vanduffel

Vrije Universiteit Brussel (VUB) ( email )

Pleinlaan 2
Brussels, Brabant 1050
Belgium

HOME PAGE: http://www.stevenvanduffel.com

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