**DISCUSSION PAPER PI-0610**

**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.