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Impact of insurance for operational risk: Is it worthwhile to insure or be insured for severe losses?

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  • Peters, Gareth W.
  • Byrnes, Aaron D.
  • Shevchenko, Pavel V.
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    Abstract

    Under the Basel II standards, the Operational Risk (OpRisk) advanced measurement approach allows a provision for reduction of capital as a result of insurance mitigation of up to 20%. This paper studies different insurance policies in the context of capital reduction for a range of extreme loss models and insurance policy scenarios in a multi-period, multiple risk setting. A Loss Distributional Approach (LDA) for modeling of the annual loss process, involving homogeneous compound Poisson processes for the annual losses, with heavy-tailed severity models comprised of [alpha]-stable severities is considered. There has been little analysis of such models to date and it is believed insurance models will play more of a role in OpRisk mitigation and capital reduction in future. The first question of interest is when would it be equitable for a bank or financial institution to purchase insurance for heavy-tailed OpRisk losses under different insurance policy scenarios? The second question pertains to Solvency II and addresses quantification of insurer capital for such operational risk scenarios. Considering fundamental insurance policies available, in several two risk scenarios, we can provide both analytic results and extensive simulation studies of insurance mitigation for important basic policies, the intention being to address questions related to VaR reduction under Basel II, SCR under Solvency II and fair insurance premiums in OpRisk for different extreme loss scenarios. In the process we provide closed-form solutions for the distribution of loss processes and claims processes in an LDA structure as well as closed-form analytic solutions for the Expected Shortfall, SCR and MCR under Basel II and Solvency II. We also provide closed-form analytic solutions for the annual loss distribution of multiple risks including insurance mitigation.

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    Bibliographic Info

    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 48 (2011)
    Issue (Month): 2 (March)
    Pages: 287-303

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    Handle: RePEc:eee:insuma:v:48:y:2011:i:2:p:287-303

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    Web page: http://www.elsevier.com/locate/inca/505554

    Related research

    Keywords: Operational risk Loss distributional approach Insurance mitigation Capital reduction [alpha]-stable Basel II Solvency II;

    References

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    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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    1. Gareth W. Peters & Pavel V. Shevchenko & Mario V. W\"uthrich, 2009. "Dynamic operational risk: modeling dependence and combining different sources of information," Papers, arXiv.org 0904.4074, arXiv.org, revised Jul 2009.
    2. Chavez-Demoulin, V. & Embrechts, P. & Neslehova, J., 2006. "Quantitative models for operational risk: Extremes, dependence and aggregation," Journal of Banking & Finance, Elsevier, Elsevier, vol. 30(10), pages 2635-2658, October.
    3. Yoshi Kawai, 2005. "IAIS and Recent Developments in Insurance Regulation," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan, Palgrave Macmillan, vol. 30(1), pages 29-33, January.
    4. McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, Elsevier, vol. 7(3-4), pages 271-300, November.
    5. Gareth W. Peters & Balakrishnan B. Kannan & Ben Lasscock & Chris Mellen & Simon Godsill, 2010. "Bayesian Cointegrated Vector Autoregression models incorporating Alpha-stable noise for inter-day price movements via Approximate Bayesian Computation," Papers, arXiv.org 1008.0149, arXiv.org.
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    Cited by:
    1. Alice X. D. Dong & Jennifer S. K. Chan & Gareth W. Peters, 2014. "Risk Margin Quantile Function Via Parametric and Non-Parametric Bayesian Quantile Regression," Papers, arXiv.org 1402.2492, arXiv.org.
    2. Gareth W. Peters & Rodrigo S. Targino & Pavel V. Shevchenko, 2013. "Understanding Operational Risk Capital Approximations: First and Second Orders," Papers, arXiv.org 1303.2910, arXiv.org.

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