It is now widely accepted that stochastic mortality – the risk that aggregate mortality might differ from that anticipated – is an important risk factor in both life insurance and pensions. As such it affects how fair values, premium rates, and risk reserves are calculated.
This paper makes use of the similarities between the force of mortality and interest rates to examine how we might model mortality risks and price mortality-related instruments using adaptations of the arbitrage-free pricing frameworks that have been developed for interest-rate derivatives. In so doing, the paper pulls together a range of arbitrage-free (or risk-neutral) frameworks for pricing and hedging mortality risk that allow for both interest and mortality factors to be stochastic. The different frameworks that we describe – short-rate models, forward-mortality models, positive-mortality models and mortality market models – are all based on positive-interest-rate modelling frameworks since the force of mortality can be treated in a similar way to the short-term risk-free rate of interest. While much of this paper is a review of the possible frameworks, the key new development is the introduction of mortality market models equivalent to the LIBOR and swap market models in the interest-rate literature.
These frameworks can be applied to a great variety of mortality-related instruments, from vanilla longevity bonds to exotic mortality derivatives.