Pricing longevity derivatives via Fourier transforms

Longevity-linked derivatives are one of the most important longevity risk management solutions for pension schemes and life annuity portfolios. In this paper, we decompose several longevity derivatives—such as geared longevity bonds and longevity-spread bonds—into portfolios involving longevity options. For instance, we show that the fair value of an index-based longevity swap can be broken down into a portfolio of long and short positions in European-style longevity caplets and floorlets, with an underlying asset equal to a population-based survivor index and strike price equal to the initial preset survivor schedule. We develop a Fourier transform approach for European-style longevity option pricing under continuous-time affine jump–diffusion models for both cohort mortality intensities and interest rates, accounting for both positive and negative jumps in mortality. The model calibration approach is described and illustrative empirical results on the valuation of longevity derivatives, using U.S. total population mortality data, are provided.