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

TL;DR

This paper analyzes the effectiveness and fairness of insurance policies for operational risk losses under Basel II and Solvency II, using advanced loss models and providing closed-form solutions for risk measures.

Contribution

It introduces novel analytical solutions for loss distributions, capital requirements, and insurance premiums in heavy-tailed operational risk models with insurance mitigation.

Findings

Insurance can reduce capital requirements under Basel II.

Analytic formulas for loss distribution and risk measures are derived.

Assessment of insurance fairness and insurer capital under different scenarios.

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.