How Robust Is the Value-at-Risk of Credit Risk Portfolios?

Forthcoming, European Journal of Finance

30 Pages Posted: 27 Feb 2015 Last revised: 2 Nov 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)

Jing Yao

Vrije Universiteit Brussel (VUB)

Date Written: October 2, 2015

Abstract

In this paper, we assess the magnitude of model uncertainty of credit risk portfolio models, i.e., what is the maximum and minimum Value-at-Risk (VaR) of a portfolio of risky loans that can be justi ed given a certain amount of available information. Puccetti and Ruschendorf (2012a) and Embrechts et al. (2013) propose the rearrangement algorithm (RA) as a general method to approximate VaR bounds when the loss distributions of the di erent loans are known but not their interdependence (unconstrained bounds). Their numerical results show that the gap between worst-case and best-case VaR is typically very high, a feature that can only be explained by lack of using dependence information. We propose a modi cation of the RA that makes it possible to approximate sharp VaR bounds when besides the marginal distributions also higher order moments of the aggregate portfolio such as variance and skewness are available as sources of dependence information. A numerical study shows that the use of moment information makes it possible to signi cantly improve the (unconstrained) VaR bounds. However, VaR assessments of credit portfolios that are performed at high con dence levels (as it is the case in Solvency II and Basel III) remain subject to signi cant model uncertainty and are not robust.

Keywords: Rearrangement algorithm, Moment bounds, Value-at-Risk, Credit risk portfolio. Minimum variance

JEL Classification: c10

Suggested Citation

Bernard, Carole and Rüschendorf, Ludger and Vanduffel, Steven and Yao, Jing, How Robust Is the Value-at-Risk of Credit Risk Portfolios? (October 2, 2015). Forthcoming, European Journal of Finance, Available at SSRN: https://ssrn.com/abstract=2570782 or http://dx.doi.org/10.2139/ssrn.2570782

Carole Bernard

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

Jing Yao (Contact Author)

Vrije Universiteit Brussel (VUB) ( email )

Pleinlaan 2
Brussels, B-1050
Belgium

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