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Model uncertainty and VaR aggregation

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  • Embrechts, Paul
  • Puccetti, Giovanni
  • Rüschendorf, Ludger

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.

Suggested Citation

  • Embrechts, Paul & Puccetti, Giovanni & Rüschendorf, Ludger, 2013. "Model uncertainty and VaR aggregation," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 2750-2764.
  • Handle: RePEc:eee:jbfina:v:37:y:2013:i:8:p:2750-2764
    DOI: 10.1016/j.jbankfin.2013.03.014
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    References listed on IDEAS

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    More about this item

    Keywords

    C6; Copula; Fréchet class; Model uncertainity; Operational Risk; Positive dependence; Rearrangement algorithm; Risk aggregation;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling

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