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Impact of Insurance for Operational Risk: Is it worthwhile to insure or be insured for severe losses?

Author

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

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 the behaviour of different insurance policies in the context of capital reduction for a range of possible extreme loss models and insurance policy scenarios in a multi-period, multiple risk settings. A Loss Distributional Approach (LDA) for modelling 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 then pertains to Solvency II and addresses what the insurers capital would be for such operational risk scenarios under different policy offerings. In addition we consider the insurers perspective with respect to fair premium as a percentage above the expected annual claim for each insurance policy. 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 process and claims process 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.

Suggested Citation

  • Gareth W. Peters & Aaron D. Byrnes & Pavel V. Shevchenko, 2010. "Impact of Insurance for Operational Risk: Is it worthwhile to insure or be insured for severe losses?," Papers 1010.4406, arXiv.org, revised Nov 2010.
  • Handle: RePEc:arx:papers:1010.4406
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    References listed on IDEAS

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    1. Yoshi Kawai, 2005. "IAIS and Recent Developments in Insurance Regulation," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 30(1), pages 29-33, January.
    2. 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 1008.0149, arXiv.org.
    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. Gareth W. Peters & Pavel V. Shevchenko & Mario V. Wuthrich, 2009. "Dynamic operational risk: modeling dependence and combining different sources of information," Papers 0904.4074, arXiv.org, revised Jul 2009.
    5. Embrechts, Paul & Neslehová, Johanna & Wüthrich, Mario V., 2009. "Additivity properties for Value-at-Risk under Archimedean dependence and heavy-tailedness," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 164-169, April.
    6. Pavel V. Shevchenko, 2010. "Implementing loss distribution approach for operational risk," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 26(3), pages 277-307, May.
    7. 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, vol. 7(3-4), pages 271-300, November.
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    Cited by:

    1. Ignatieva, Katja & Landsman, Zinoviy, 2019. "Conditional tail risk measures for the skewed generalised hyperbolic family," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 98-114.
    2. Guillén, Montserrat & Sarabia, José María & Prieto, Faustino, 2013. "Simple risk measure calculations for sums of positive random variables," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 273-280.

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