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

Published online by Cambridge University Press:  17 April 2015

Andrew J.G. Cairns ,
David Blake  and
Kevin Dowd
Andrew J.G. Cairns
Affiliation:
Department of Actuarial Mathematics and Statistics, School of Mathematical and Computer Sciences, Heriot-Watt University Edinburgh, EH14 4AS, United Kingdom, E-mail: [email protected]
David Blake
Affiliation:
Pensions Institute Cass Business School, 106 Bunhill Row, London, EC1Y 8TZ, United Kingdom
Kevin Dowd
Affiliation:
Centre for Risk & Insurance Studies, Nottingham University Business School, Jubilee Campus, Nottingham, NG8 1BB, United Kingdom
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Abstract

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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.

Keywords

Stochastic mortalityterm structure of mortalitysurvivor indexspot survival probabilitiesspot force of mortalityforward mortality surfaceshort-rate modelsforward mortality modelspositive mortality frameworkmortality market modelsannuity market modelSCOR market model
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 36 , Issue 1 , May 2006 , pp. 79 - 120
Copyright
Copyright © ASTIN Bulletin 2006

Footnotes

*

First version presented at the 14th International AFIR Colloquium, Boston, 2004, under the title Pricing Frameworks for Securitization of Mortality Risk, available online at http://afir2004.soa.org/afir_papers.htm.

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