Value-at-Risk Bounds with Two-Sided Dependence Information

38 Pages Posted: 14 Dec 2017

See all articles by Thibaut Lux

Thibaut Lux

Vrije Universiteit Brussels

Ludger Rüschendorf

University of Freiburg

Multiple version iconThere are 2 versions of this paper

Date Written: April 11, 2017

Abstract

Value-at-Risk bounds for aggregated risks have been derived in the literature in settings where besides the marginal distributions of the individual risk factors one-sided bounds for the joint distribution respectively the copula of the risks are available. In applications it turns out that these improved standard bounds on Value-at-Risk tend to be too wide to be relevant for practical applications, especially when the number of risk factors is large or when the dependence restriction is not strong enough. In this paper, we develop a method to compute Value-at-Risk bounds when besides the marginal distributions of the risk factors, two-sided dependence information in form of an upper and a lower bound on the copula of the risk factors is available. The method is based on a relaxation of the exact dual bounds which we derive by means of the Monge–Kantorovich transportation duality. In several applications we illustrate that two-sided dependence information typically leads to strongly improved bounds on the Value-at-Risk of aggregations.

Keywords: model uncertainty, copulas, duality theory, value-at-risk

JEL Classification: C02, C63, D80, G31

Suggested Citation

Lux, Thibaut and Rüschendorf, Ludger, Value-at-Risk Bounds with Two-Sided Dependence Information (April 11, 2017). Available at SSRN: https://ssrn.com/abstract=3086256 or http://dx.doi.org/10.2139/ssrn.3086256

Thibaut Lux (Contact Author)

Vrije Universiteit Brussels ( email )

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

Ludger Rüschendorf

University of Freiburg ( email )

Fahnenbergplatz
Freiburg, D-79085
Germany

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
48
Abstract Views
324
PlumX Metrics