Estimating the probability of insurance recovery in operational risk

Ruben D Cohen, Jonathan Humphries and Jia Lu

Journal of Operational Risk

Abstract: Insurance can effectively mitigate significant operational risks. However, not all losses are insurable, and payments of covered losses are not generally reimbursed in full for reasons including the chosen limits of cover as well as risks or exposures that may be excluded from the coverage. When incorporating insurance into a firm’s operational risk model, the risk mitigation calculation needs to appropriately reflect the insurance coverage afforded in a framework that is well reasoned and documented, demonstrating that the calculation is timely aligned to the institution’s operational risk profile, and that the institution’s methodology for recognizing insurance captures all the relevant elements through discounts or haircuts in the amount of insurance recognition. Haircuts (or discounts) can emanate from, for example, mismatches in cover, uncertainty over payment and policy terms and conditions, all of which are often difficult to estimate because of the ambiguities around policy coverage and terms and conditions when considered in the context of operational risk loss events. A dominant source of these haircuts is policy wording, which consists of the insuring clauses, definitions and exclusions that define the scope of coverage. In insurance modeling, the effects of these haircuts are generally lumped into a single parameter known as the probability of insurance recovery (PoIR). Given the apparent lack of any previous modeling efforts in the public domain that aim to estimate the PoIR, we must start somewhere. The aim of this paper is to introduce an underlying methodology. We first address the building blocks of the PoIR and then integrate them into the risk taxonomy of a firm or unit of measure with a view to incorporating the outcome into the insurance and capital models.

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