Probability of Sufficiency of Solvency II Reserve Risk Margins: Practical Approximations

The new Solvency II regime and the upcoming IFRS 4 Phase II regime bring significant changes to current reporting of insurance entities, and particularly in relation to valuation of insurance liabilities. Insurers will be required to valuate their insurance liabilities on a risk-adjusted basis to allow for uncertainty inherent in cash flows that arise from the liability of insurance contracts. Whilst most European-based insurers are expected to adopt the Cost of Capital (CoC) approach to calculating reserve risk margin - the risk adjustment method commonly agreed under Solvency II and IFRS 4 Phase II, there is one additional requirement of IFRS to also disclose confidence level of the risk margin. Given there is no specific guidance on the calculation of confidence level, the purpose of this paper is to explore and examine practical ways of estimating the risk margin confidence level measured by Probability of Sufficiency (PoS). The paper provides some practical approximation formulae that would allow one to quickly estimate the implied PoS of Solvency II risk margin for a given non-life insurance liability, the risk profile of which is specified by the type and characteristics of the liability (e.g. type/nature of business, liability duration and convexity, etc.), which in turn are associated with: the level of variability measured by Coefficient of Variation (CoV); the degree of Skewness per unit of CoV; and the degree of Kurtosis per unit of CoV squared.The approximation formulae of PoS are derived for both the standalone class risk margin and the diversified risk margin at the portfolio level.