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Pricing Death: Frameworks for the Valuation and Securitization
of Mortality Risk

Andrew J.G. Cairns, David Blake, and Kevin Dowd

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 a®ects 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 di®erent 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.

Keywords: stochastic mortality, term structure of mortality, survivor index,
spot survival probabilities, spot force of mortality, forward mortality surface,
short-rate models, forward mortality models, positive mortality framework,
mortality market models, annuity market model, SCOR market model.