A market- and time-consistent extension for the EIOPA risk-margin

In this paper, we investigate market- and time-consistent valuation of life-insurance liabilities, which are long-dated by nature. To obtain a market- and time-consistent value, the “two-step market evaluation” introduced by Pelsser and Stadje (Math Finance 24:25–65, 2014) is used to evaluate a hybrid payoff with underlying hedgeable financial and (partially) unhedgeable actuarial risks. The resulting time-consistent and market-consistent (TCMC) price captures the dynamics of the risk drivers over the lifetime of the contract. We show that the EIOPA standard-formula for the risk-margin is not time-consistent, and we construct a time-consistent version of the risk-margin that captures the extra uncertainties from the process dynamics. EIOPA’s standard-formula for the Risk-Margin is compared to the TCMC price for a simple unit-linked contract and we show that the effects of time-inconsistency are increasing with maturity and are significant for long-dated contracts.