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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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    1. Hobæk Haff, Ingrid & Aas, Kjersti & Frigessi, Arnoldo, 2010. "On the simplified pair-copula construction -- Simply useful or too simplistic?," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1296-1310, May.
    2. Puccetti Giovanni & Rüschendorf Ludger, 2012. "Bounds for joint portfolios of dependent risks," Statistics & Risk Modeling, De Gruyter, vol. 29(2), pages 107-132, June.
    3. Marco Moscadelli, 2004. "The modelling of operational risk: experience with the analysis of the data collected by the Basel Committee," Temi di discussione (Economic working papers) 517, Bank of Italy, Economic Research and International Relations Area.
    4. Pérignon, Christophe & Smith, Daniel R., 2010. "The level and quality of Value-at-Risk disclosure by commercial banks," Journal of Banking & Finance, Elsevier, vol. 34(2), pages 362-377, February.
    5. Mainik, Georg & Embrechts, Paul, 2013. "Diversification in heavy-tailed portfolios: properties and pitfalls," Annals of Actuarial Science, Cambridge University Press, vol. 7(1), pages 26-45, March.
    6. Ruodu Wang & Liang Peng & Jingping Yang, 2013. "Bounds for the sum of dependent risks and worst Value-at-Risk with monotone marginal densities," Finance and Stochastics, Springer, vol. 17(2), pages 395-417, April.
    7. Mainik Georg & Rüschendorf Ludger, 2012. "Ordering of multivariate risk models with respect to extreme portfolio losses," Statistics & Risk Modeling, De Gruyter, vol. 29(1), pages 73-106, March.
    8. Klaus Bocker & Claudia Kluppelberg, 2010. "Multivariate models for operational risk," Quantitative Finance, Taylor & Francis Journals, vol. 10(8), pages 855-869.
    9. Embrechts, Paul & Puccetti, Giovanni, 2010. "Bounds for the sum of dependent risks having overlapping marginals," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 177-190, January.
    10. Georg Mainik & Ludger Rüschendorf, 2010. "On optimal portfolio diversification with respect to extreme risks," Finance and Stochastics, Springer, vol. 14(4), pages 593-623, December.
    11. Embrechts, Paul & Hoing, Andrea & Puccetti, Giovanni, 2005. "Worst VaR scenarios," Insurance: Mathematics and Economics, Elsevier, vol. 37(1), pages 115-134, August.
    12. Wang, Bin & Wang, Ruodu, 2011. "The complete mixability and convex minimization problems with monotone marginal densities," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1344-1360, November.
    13. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: theory," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 3-33, August.
    14. Arbenz, Philipp & Hummel, Christoph & Mainik, Georg, 2012. "Copula based hierarchical risk aggregation through sample reordering," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 122-133.
    15. Paul Embrechts & Giovanni Puccetti, 2006. "Aggregating risk capital, with an application to operational risk," The Geneva Papers on Risk and Insurance Theory, Springer;International Association for the Study of Insurance Economics (The Geneva Association), vol. 31(2), pages 71-90, December.
    16. L. Rüschendorf, 1983. "Solution of a statistical optimization problem by rearrangement methods," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 30(1), pages 55-61, December.
    17. Mesfioui, Mhamed & Quessy, Jean-Francois, 2005. "Bounds on the value-at-risk for the sum of possibly dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 37(1), pages 135-151, August.
    18. Paul Embrechts & Giovanni Puccetti, 2006. "Bounds for Functions of Dependent Risks," Finance and Stochastics, Springer, vol. 10(3), pages 341-352, September.
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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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