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Aggregating risk capital, with an application to operational risk

Author

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  • Paul Embrechts

    (Department of Mathematics, ETH Zurich, CH-8092 Zurich, Switzerland, e-mail: embrechts@math.ethz.ch)

  • Giovanni Puccetti

    (Department of Mathematics for Decisions, University of Firenze, 50134 Firenze, Italy, e-mail: giovanni.puccetti@dmd.unifi.it)

Abstract

We describe a numerical procedure to obtain bounds on the distribution function of a sum of n dependent risks having fixed marginals. With respect to the existing literature, our method provides improved bounds and can be applied also to large non-homogeneous portfolios of risks. As an application, we compute the VaR-based minimum capital requirement for a portfolio of operational risk losses. The Geneva Risk and Insurance Review (2006) 31, 71–90. doi:10.1007/s10713-006-0556-6

Suggested Citation

  • Paul Embrechts & Giovanni Puccetti, 2006. "Aggregating risk capital, with an application to operational risk," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 31(2), pages 71-90, December.
    • Handle: RePEc:pal:genrir:v:31:y:2006:i:2:p:71-90
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    References listed on IDEAS

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    1. Rosenberg, Joshua V. & Schuermann, Til, 2006. "A general approach to integrated risk management with skewed, fat-tailed risks," Journal of Financial Economics, Elsevier, vol. 79(3), pages 569-614, March.
    2. Paul Embrechts & Giovanni Puccetti, 2006. "Bounds for Functions of Dependent Risks," Finance and Stochastics, Springer, vol. 10(3), pages 341-352, September.
    3. Chavez-Demoulin, V. & Embrechts, P. & Neslehova, J., 2006. "Quantitative models for operational risk: Extremes, dependence and aggregation," Journal of Banking & Finance, Elsevier, vol. 30(10), pages 2635-2658, October.
    4. Embrechts, Paul & Hoing, Andrea & Puccetti, Giovanni, 2005. "Worst VaR scenarios," Insurance: Mathematics and Economics, Elsevier, vol. 37(1), pages 115-134, August.
    5. Denuit, M. & Genest, C. & Marceau, E., 1999. "Stochastic bounds on sums of dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 25(1), pages 85-104, September.
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    Cited by:

    1. Bignozzi, Valeria & Puccetti, Giovanni & Rüschendorf, Ludger, 2015. "Reducing model risk via positive and negative dependence assumptions," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 17-26.
    2. Embrechts, Paul & Puccetti, Giovanni & Rüschendorf, Ludger, 2013. "Model uncertainty and VaR aggregation," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 2750-2764.
    3. Dominik D. Lambrigger & Pavel V. Shevchenko & Mario V. Wuthrich, 2009. "The Quantification of Operational Risk using Internal Data, Relevant External Data and Expert Opinions," Papers 0904.1361, arXiv.org.
    4. Albrecht, Peter & Schwake, Edmund & Winter, Peter, 2007. "Quantifizierung operationeller Risiken: Der Loss Distribution Approach," German Risk and Insurance Review (GRIR), University of Cologne, Department of Risk Management and Insurance, vol. 3(1), pages 1-45.
    5. Paul Embrechts, 2009. "Copulas: A Personal View," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(3), pages 639-650, September.
    6. Berger, Allen N. & Curti, Filippo & Mihov, Atanas & Sedunov, John, 2022. "Operational Risk is More Systemic than You Think: Evidence from U.S. Bank Holding Companies," Journal of Banking & Finance, Elsevier, vol. 143(C).
    7. 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.
    8. Enrique Jiménez-Rodríguez & José Manuel Feria-Domínguez & Alonso Sebastián-Lacave, 2018. "Assessing the Health-Care Risk: The Clinical-VaR, a Key Indicator for Sound Management," IJERPH, MDPI, vol. 15(4), pages 1-17, March.
    9. Raphael Hauser & Sergey Shahverdyan & Paul Embrechts, 2014. "A General Duality Relation with Applications in Quantitative Risk Management," Papers 1410.0852, arXiv.org.
    10. Archil Gulisashvili & Peter Tankov, 2013. "Tail behavior of sums and differences of log-normal random variables," Papers 1309.3057, arXiv.org, revised Jan 2016.
    11. Lu, Zhaoyang, 2011. "Modeling the yearly Value-at-Risk for operational risk in Chinese commercial banks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(4), pages 604-616.
    12. Azamat Abdymomunov & Filippo Curti, 2020. "Quantifying and Stress Testing Operational Risk with Peer Banks’ Data," Journal of Financial Services Research, Springer;Western Finance Association, vol. 57(3), pages 287-313, June.
    13. Robert Jarrow & Jeff Oxman & Yildiray Yildirim, 2010. "The cost of operational risk loss insurance," Review of Derivatives Research, Springer, vol. 13(3), pages 273-295, October.
    14. Sonia Benito Muela & Carmen López-Martín, 2023. "A Comparison of Information Criterion for Choosing Copula Models," International Business Research, Canadian Center of Science and Education, vol. 16(4), pages 1-1, April.
    15. Antoni Ferri & Lluís Bermúdez & Montserrat Guillén, 2012. "How to use the standard model with own data?," Working Papers XREAP2012-03, Xarxa de Referència en Economia Aplicada (XREAP), revised Feb 2012.

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