Pricing Frameworks for Securitization of Mortality Risk1

It is now an accepted fact that stochastic mortality – the risk that future trends in mortality are different from those anticipated – is an important risk factor in both life insurance and pensions. As a risk factor it affects how we calculate fair values, premium rates, and risk reserves. In this paper we discuss theoretical frameworks and models for pricing mortality derivatives and valuing liabilities which incorporate mortality guarantees. Models developed within one of these frameworks also facilitate the calculation of risk (or quantile) reserves and in a way that is consistent with an arbitrage-free pricing framework. The objective of the paper is to provide a foundation for further work which will look at the practical development and implementation of such models. The different frameworks that we describe 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. The frameworks discussed are short-rate models, forward-mortality models, positive-mortality models and mortality market models.