Market-consistent valuation of pension liabilities

Pension funds and life insurance companies have liabilities on their books with extremely long-dated maturities that are exposed to non-hedgeable actuarial risks and also to market risks. In this paper, we show that it is computationally feasible to price pensions contracts in an incomplete market setting with time-consistent and market-consistent (TCMC) pricing operators. Furthermore, we compare the TCMC prices for life-insurance and pension contracts to alternative pricing methods that are currently used for pricing pension and life-insurance liabilities: the best estimate pricing method which is typically used for pension liabilities, and the EIOPA’s risk margin method that is used under Solvency II to value life-insurance liabilities. We show that the best estimate pricing method completely ignores the uncertainty in the non-hedgeable risks. We also show that the risk margin method is a significant step in the right direction to reflect most of this uncertainty in the pricing. However, the risk margin price still ignores some uncertainties, and is therefore not fully time-consistent. For long-dated contracts this effect should not be ignored.