Semicoherent Multipopulation Mortality Modeling: The Impact on Longevity Risk Securitization

Multipopulation mortality models play an important role in longevity risk transfers involving more than one population. Most of the existing multi‐population mortality models are built on the hypothesis of coherence, which assumes that there always exists a force that brings the mortality differential between any two populations back to a constant long‐term equilibrium level. This hypothesis prevents diverging long‐term forecasts, which do not seem to be biologically reasonable. However, the coherence assumption may be perceived by market participants as too strong and is in fact not always supported by empirical observations. In this article, we introduce a new concept called ‘semicoherence,’ which is less stringent in the sense that it permits the mortality trajectories of two related populations to diverge, as long as the divergence does not exceed a specific tolerance corridor, beyond which mean reversion will come into effect. We further propose to produce semicoherent mortality forecasts by using a vector threshold autoregression. The proposed modeling approach is illustrated with mortality data from U.S. and English and Welsh male populations, and is applied to several pricing and hedging scenarios.