Model Uncertainty and VaR Aggregation

19 Pages Posted: 16 Oct 2014

See all articles by Paul Embrechts

Paul Embrechts

Swiss Federal Institute of Technology Zurich; Swiss Finance Institute

Giovanni Puccetti

University of Milan - Department of Economics, Management and Quantitative Methods (DEMM)

Ludger Rüschendorf

University of Freiburg

Date Written: 2013

Abstract

Despite well-known shortcomings as a risk measure, Value-at-Risk (VaR) is still the industry and regulatory standard for the calculation of risk capital in banking and insurance. This paper is concerned with the numerical estimation of the VaR for a portfolio position as a function of different dependence scenarios on the factors of the portfolio. Besides summarizing the most relevant analytical bounds, including a discussion of their sharpness, we introduce a numerical algorithm which allows for the computation of reliable (sharp) bounds for the VaR of high-dimensional portfolios with dimensions d possibly in the several hundreds. We show that additional positive dependence information will typically not improve the upper bound substantially. In contrast higher order marginal information on the model, when available, may lead to strongly improved bounds. Several examples of practical relevance show how explicit VaR bounds can be obtained. These bounds can be interpreted as a measure of model uncertainty induced by possible dependence scenarios.

Keywords: Copula, Fréchet class, Model Uncertainty, Operational Risk, Positive Dependence, Rearrangement Algorithm, Risk Aggregation, Value-at-Risk, VaR-bounds.

JEL Classification: 91G60, 91B30

Suggested Citation

Embrechts, Paul and Puccetti, Giovanni and Rüschendorf, Ludger, Model Uncertainty and VaR Aggregation (2013). Journal of Banking and Finance, Vol. 37, No. 8, 2013, Available at SSRN: https://ssrn.com/abstract=2510295

Paul Embrechts

Swiss Federal Institute of Technology Zurich ( email )

ETH-Zentrum
CH-8092 Zurich
Switzerland

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

Giovanni Puccetti (Contact Author)

University of Milan - Department of Economics, Management and Quantitative Methods (DEMM) ( email )

Via Conservatorio, 7
Milan, 20122
Italy

Ludger Rüschendorf

University of Freiburg ( email )

Fahnenbergplatz
Freiburg, D-79085
Germany

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