Pricing longevity-linked securities in the absence of a liquid and complete market for longevity risk raises many challenges. Most of the proposed pricing approaches are based on stochastic mortality models in which the time-dependent parameters are projected into the future. Naturally, these approaches are affected by model risk as any structural shortcoming of the underlying simulation model might lead to inadequate prices. As argued by several authors in the field of longevity trend modeling, long-term mortality projections should account for the risk of unanticipated mortality trend changes.
Therefore, we implement two promising and widely adopted pricing approaches in a stochastic modeling framework which explicitly considers the risk of random future mortality trend changes: the risk-adjusted pricing approach based on a pricing measure and the cost of capital approach inspired by capital requirements for (re)insurers under modern risk-based solvency regimes. Our setup allows for potential socioeconomic mortality differentials from the underlying long-term mortality trend and is therefore applicable to both customized and index-based instruments. A discussion of both pricing approaches is provided with regard to their economic justification, practical applicability, and calibration. In a numerical application, we derive forward rates for customized and index-based longevity swaps and demonstrate that the implemented approaches produce plausible risk loadings.