Pricing S-forwards via the Risk Margin under Solvency II

The paper focuses on the securitization of longevity risk via longevity-linked securities. Among the ones proposed in the literature, we consider the S-forward, an agreement between two counterparties to exchange at the maturity a fixed survival-dependent payment for a payment depending on the realized survival of a given cohort of individuals. S-forwards are up to now the most prevalent securities in the longevity market. Major problems are encountered in the pricing of these derivatives, mainly due to the incompleteness of the longevity market which does not allow to find a unique market price of risk. We propose here a method to find a maximum market price for longevity risk depending on the risk margin implicit in the calculation of the technical provisions as defined in the Solvency II project. We adopt the Cairns-Black-Dowd model to represent the evolution of mortality over time, that combined with the information on the risk margin permits 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.