Probability of Sufficiency of the Risk Margin for Life Companies Under IFRS 17

Abstract

With the upcoming IFRS 17 regime, significant changes for the valuation of insurance liabilities can be expected. Insurers will be required to evaluate their insurance liabilities on a risk-adjusted basis to allow for uncertainty inherent in cash flows that arise from the liability of insurance contracts. In addition to the changes in estimating insurance liabilities as compared to IFRS 4, there is a specific requirement of IFRS 17 to disclose “the confidence level used to determine the risk adjustment for non-financial risk. If the entity uses a technique other than the confidence level technique for determining the risk adjustment for non-financial risk, it shall disclose the technique used and the confidence level corresponding to the results of that technique” (extract from IFRS 17).

Given that there is no specific guidance on the calculation of confidence level when using a technique other than the confidence level (e.g. Expected Shortfall or Cost of Capital), the purpose of this article is to propose a method that can be applied to life insurance contract portfolios to estimate the confidence level as required. The proposed method will be using only the basic characteristics (e.g. CoV and relative Skewness) of the main life insurance risk drivers without resorting to heavy modelling/simulations. In order to achieve this goal, this article proposes to model the two main risks present in a life insurance portfolio: • the interest rate related risk based on duration/convexity models and interest rate models, assuming that the company uses a replicating portfolio approach for modelling its liability cash-flows; • the biometric risk based on parametric models on which a few issues need to be resolved: o The calibration of the model on an ultimate view starting from a one-year view (e.g. when using the solvency 2 standard formula). o The need to separately model the different biometric risks (mortality, longevity, morbidity, etc.).

On the basis of these models, it is possible to estimate the characteristics below for the two risks (biometric and interest rate): • 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 CoV2.

The resulting distributions will then be aggregated using the Fleishman polynomials. As a result, the approximation formulae as described in Dal Moro/Krvavych (2017) can be applied for the diversified risk margin at the portfolio level. Using these formulae, the confidence level is easily estimated.

Keywords: IFRS 17, Confidence Level, Cost of Capital, Probability of Sufficiency, Duration, Convexity, Interest Rate, Biometric Risk, Replicating Portfolio

JEL Classification: G22, E22