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Under the Basel II standards, the Operational Risk (OpRisk) advancedmeasurement approach allows a provision for reduction of capital as a result ofinsurance mitigation of up to 20%. This paper studies the behaviour ofdifferent insurance policies in the context of capital reduction for a range ofpossible extreme loss models and insurance policy scenarios in a multi-period,multiple risk settings. A Loss Distributional Approach (LDA) for modelling ofthe annual loss process, involving homogeneous compound Poisson processes forthe annual losses, with heavy tailed severity models comprised of alpha-stableseverities is considered. There has been little analysis of such models to dateand it is believed, insurance models will play more of a role in OpRiskmitigation and capital reduction in future. The first question of interest iswhen would it be equitable for a bank or financial institution to purchaseinsurance for heavy tailed OpRisk losses under different insurance policyscenarios? The second question then pertains to Solvency II and addresses whatthe insurers capital would be for such operational risk scenarios underdifferent policy offerings. In addition we consider the insurers perspectivewith respect to fair premium as a percentage above the expected annual claimfor each insurance policy. The intention being to address questions related toVaR reduction under Basel II, SCR under Solvency II and fair insurance premiumsin OpRisk for different extreme loss scenarios. In the process we provideclosed form solutions for the distribution of loss process and claims processin an LDA structure as well as closed form analytic solutions for the ExpectedShortfall, SCR and MCR under Basel II and Solvency II. We also provide closedform analytic solutions for the annual loss distribution of multiple risksincluding insurance mitigation.

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