Longevity risk hedging and basisi risk.

The improvements of longevity are intensifying the need for capital markets to be used to manage and transfer the risk through longevity-linked securities. Nevertheless the difference between the reference population of the hedging instrument ("hedging population") and the population of members of a pension plan or the beneficiaries of an annuity portfolio ("exposed population") determines a signicant heterogeneity which causes the so-called basis risk. The paper focuses on the longevity risk management by securitization, providing a framework for measuring the basis risk impact on the hedging strategies. To this aim we propose a model that measure the population basis risk involved in a longevity hedge, in the functional demographic model (FDM) setting.In order to quantify the basis risk, we define a stochastic mortality model for two populations based on the FDM framework. We consider both an independent FDM (the hedging population is independent from the exposed population) and a joint FDM (both populations are jointly driven by a single index of mortality over time). Under the proposed mortality model, we build a longevity hedging strategy involving a portfolio of q-forwards calibrated through the key-q-duration (KQD), i.e. the annuity portfolios price sensitivity to a shift in a key mortality rate . The shifts are adjusted with the standard deviation of the exposed population mortality in order to realise a more effective hedge. In order to analyse the hedge effectiveness we consider the present value of both unexpected cash flows of the insurance portfolio and payoffs from the q-forwards involved in the hedging portfolio. The KQD of these quantities as well as an adjustment factor depending on the specified mortality model allow to find the required notional amount of the q-forwards in presence of basis risk.