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Multivariate VaRs for Operational Risk Capital Computation: a Vine Structure Approach

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Abstract

The Basel Advanced Measurement Approach requires financial institutions to compute capital requirements on internal data sets. In this paper we introduce a new methodology permitting capital requirements to take into account the embedded dependence structures of operational risks. The loss distributions are provided in a matrix of 56 cells. Constructing a vine architecture, which is a bivariate decomposition of a n-dimensional structure (n > 2), we use this approach to compute multivariate operational risk VaRs. We analyse the results and compare them with classical methodologies based on LDF modelings. Our method is simple to carry out, easy to interpret and complies with the new Basel Committee requirements

Suggested Citation

  • Dominique Guegan & Bertrand Hassani, 2011. "Multivariate VaRs for Operational Risk Capital Computation: a Vine Structure Approach," Documents de travail du Centre d'Economie de la Sorbonne 11017rr, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Apr 2012.
    • Handle: RePEc:mse:cesdoc:11017rr
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    1. Dominique Guegan & Bertrand Hassani & Cédric Naud, 2010. "An efficient threshold choice for operational risk capital computation," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00544342, HAL.
    2. Dominique Guegan & Pierre-André Maugis, 2008. "New prospects on vines," Documents de travail du Centre d'Economie de la Sorbonne b08095, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Mar 2010.
    3. Dominique Guegan & Bertrand K. Hassani, 2011. "Operational risk: a Basel II++ step before Basel III," Documents de travail du Centre d'Economie de la Sorbonne 11053, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    4. Dominique Guegan & Bertrand Hassani & Cédric Naud, 2011. "An efficient threshold choice for operational risk capital computation," Post-Print halshs-00790217, HAL.
    5. Kjersti Aas & Daniel Berg, 2009. "Models for construction of multivariate dependence - a comparison study," The European Journal of Finance, Taylor & Francis Journals, vol. 15(7-8), pages 639-659.
    6. Dominique Guegan & Pierre-André Maugis, 2010. "An Econometric Study of Vine Copulas," Documents de travail du Centre d'Economie de la Sorbonne 10040, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    7. Hüsler, Jürg & Reiss, Rolf-Dieter, 1989. "Maxima of normal random vectors: Between independence and complete dependence," Statistics & Probability Letters, Elsevier, vol. 7(4), pages 283-286, February.
    8. Aas, Kjersti & Czado, Claudia & Frigessi, Arnoldo & Bakken, Henrik, 2009. "Pair-copula constructions of multiple dependence," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 182-198, April.
    9. Dominique Guegan & Pierre-André Maugis, 2010. "New Prospects on Vines," Post-Print halshs-00348884, HAL.
    10. Dominique Guegan & Bertrand Hassani, 2009. "A modified Panjer algorithm for operational risk capital calculations," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00443846, HAL.
    11. Dominique Guegan & Bertrand Hassani, 2011. "Operational risk: A Basel II++ step before Basel III," Post-Print halshs-00639484, HAL.
    12. Dominique Guegan & Bertrand Hassani, 2009. "A modified Panjer algorithm for operational risk capital calculations," Post-Print halshs-00443846, HAL.
    13. Dominique Guegan & Pierre-André Maugis, 2011. "An econometric Study for Vine Copulas," Post-Print halshs-00645799, HAL.
    14. Patricia Mariela Morillas, 2005. "A method to obtain new copulas from a given one," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 61(2), pages 169-184, April.
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    More about this item

    Keywords

    Operational risks; vine copula; loss distribution function; nested structure; VaR;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling

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