Model Uncertainty and VaR Aggregation
19 Pages Posted: 16 Oct 2014
Date Written: 2013
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: Suggested Citation