A longevity basis risk analysis in a joint FDM framework

The innovative contribution of the paper occurs in two key points: the modelling of mortality and the hedging strategy. Regarding the first point, the paper proposes a functional demographic model framework (FDMF) for capturing the basis risk. The FDMF model generally designed for single population combines functional data analysis, nonparametric smoothing and robust statistics. It allows to capture the variability of the mortality trend, by separating out the effects of several orthogonal components. The novelty is to set the FDMF for modelling the mortality of the two populations, the hedging and the exposed one. Regarding the second point, the basic idea is to calibrate the hedging strategy determining a suitable mixture of q-forwards linked to mortality rates to maximise the degree of longevity risk reduction. This calibration is based on the key q-duration intended as a measure allowing to estimate the price sensitivity of the annuity portfolio to the changes in the underlying mortality curve.