Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-26T04:58:58.716Z Has data issue: false hasContentIssue false
  • English
  • Français

Asymptotics for Operational Risk Quantified with Expected Shortfall

Published online by Cambridge University Press:  09 August 2013

Francesca Biagini  and
Sascha Ulmer
Francesca Biagini
Affiliation:
Department of Mathematics, LMU, Theresienstr. 39, D-80333 Munich, Germany, Fax: +49 89 2180 4452, E-Mail: [email protected]
Sascha Ulmer
Affiliation:
E-Mail: [email protected].
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we estimate operational risk by using the convex risk measure Expected Shortfall (ES) and provide an approximation as the confidence level converges to 100% in the univariate case. Then we extend this approach to the multivariate case, where we represent the dependence structure by using a Lévy copula as in Böcker and Klüppelberg (2006) and Böcker and Klüppelberg, C. (2008). We compare our results to the ones obtained in Böcker and Klüppelberg (2006) and (2008) for Operational VaR and discuss their practical relevance.

Keywords

Operational riskExpected ShortfallLévy copularegular variation
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 39 , Issue 2 , November 2009 , pp. 735 - 752
Copyright
Copyright © International Actuarial Association 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Basel Committee of Banking Supervision (2004). International Convergence of Capital Measurement and Capital Standards. Basel. Available at www.bis.org.Google Scholar
Bingham, N.H., Goldie, C.M. and Teugels, J.L. (1987) Regular Variation. Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Böcker, K. (2006) Operational Risk: analytical results when high-severity losses follow a generalized Pareto distribution (GDP) – a note. Journal of Risk 8, 1–4.Google Scholar
Böcker, K. and Klüppelberg, C. (2005) Operational VaR: a closed-form solution. RISK Magazine, December, 90–93.Google Scholar
Böcker, K. and Klüppelberg, C. (2006) Multivariate models for operational risk. Accepted for publication in Quantitative Finance.Google Scholar
Böcker, K. and Klüppelberg, C. (2007) Multivariate Operational Risk: Dependence Modelling with Lévy Copulas. 2007 ERM Symposium Online Monograph, Society of Actuaries, and Joint Risk Management section newsletter of the Society of Actuaries, Casualty of Actuaries, and Canadian Institute of Actuaries Society of Actuaries.Google Scholar
Böcker, K. and Klüppelberg, C. (2008) Modelling and Measuring Multivariate Operational Risk with Lévy Copulas. J. Operational Risk 3(2), 3–27.Google Scholar
Chavez-Demoulin, V. and Embrechts, P. (2004) Advanced Extremal Models for Operational Risk. Tech. rep. ETH Zürich. Available at www.math.ethz.ch.Google Scholar
Embrechts, P., Klüppelberg, C. and Mikosch, T. (1997) Modelling Extremal Events for Insurance and Finance. Springer, Berlin.Google Scholar
Federal Office of Private Insurance (2006) Technisches Dokument zum Swiss Solvency Test. Bern. Available at www.bpv.admin.ch.Google Scholar
Föllmer, H. and Schied, A. (2004) Stochastic Finance. deGruyter, Berlin.Google Scholar
Kallsen, J. and Tankov, P. (2004) Characterization of dependence of multidimensional Lévy processes using Lévy copulas. Journal of Multivariate Analysis 97, 1551–1572.Google Scholar
McNeil, A.J., Frey, R. and Embrechts, P. (2005) Quantitative Risk Management. Princeton University Press, Princeton and Oxford.Google Scholar
Moscadelli, M. (2004) The modelling of operational risk: experience with the analysis of the data collected by the Basel Committee. Banca D'Italia, Termini di discussione No. 517.Google Scholar
Nešlehová, J., Embrechts, P. and Chavez-Demoulin, V. (2006) Infinite mean models and the LDA for operational risk. Journal of Operational Risk, 1(1), 3–25.Google Scholar
Resnick, S.I. (1987) Extreme Values, Regular Variation, and Point Processes. Springer, New York.Google Scholar
Ulmer, S.I. (2007) Ein mehrdimensionales Modell für operationelles Risiko quantifiziert durch den Expected Shortfall, Diplomarbeit, available at www.math.lmu.de/~sekrfil/diplomarbeiten.html.Google Scholar