Maximum Market Price of Longevity Risk Under Solvency Regimes: The Case Of Solvency II

Abstract

Longevity risk constitutes an important risk factor for life insurance companies and it can be managed through longevity-linked securities. The market of longevity-linked securities is at present far from being complete and does not allow to find a unique pricing measure. We propose a method to estimate the maximum market price of longevity risk depending on the risk margin implicit within the calculation of the technical provisions as defined by Solvency II. The maximum price of longevity risk is determined for a survivor forward (S-forward), an agreement between two counterparties to exchange at maturity a fixed survival-dependent payment for a payment depending on the realized survival of a given cohort of individuals. The maximum prices determined for the S-forwards can be used to price other longevity-linked securities, such as q-forwards. The Cairns-Blake-Dowd model is used to represent the evolution of mortality over time, that combined with the information on the risk margin, enables us to calculate upper limits for the risk-adjusted survival probabilities, the market price of longevity risk and the S-forward prices. Numerical results can be extended for the pricing of other longevity-linked securities.