A Solution for Solvency II Quantitative Requirements Modeling with Long-Tail Liabilities

The European Parliament’s SolvencyII Directive introduced a new regulation for insurance and reinsurancebusiness designed to establish a consistently improved level of policyholder protection by means of a three-pillar process. Pillar 1 of the directive contains quantitative requirements for the insurance industry in respect to technical provisions (TPs) and the solvency capital requirement(SCR). The cornerstone of SolvencyII one-year risk horizon is the Fair Valueof Liabilities (FVL). The SCR and Economic Balance Sheetat inception should be able to withstand a first future calendar year in distress (at the level of 1-in-200-year event). We provide a rigorous statistical treatment of the risk metricsrequired to fulfil SolvencyII requirements for internal modelsapplicable to reserve risk with long-tailliabilities. The proposed internal modelis novel in not relying on the proportionality proxy. A tractable simulation based solution ensures adequate capital to restore the economic balance sheetto...