Modelling and Management of Mortality Risk: A Review
Andrew J.G. Cairns
David Blake
Kevin Dowd
First version: December 2007
This version: May 22, 2008

Abstract

In the first part of the paper, we consider the wide range of extrapolative stochastic mortality models that have been proposed over the last 15 to 20 years. A number of models that we consider are framed in discrete time and place emphasis on the statistical aspects of modelling and forecasting.

We discuss how these models can be evaluated, compared and contrasted. We also discuss a discrete-time market model that facilitates valuation of mortality-linked contracts with embedded options. We then review several approaches to modelling mortality in continuous time.

These models tend to be simpler in nature, but make it possible to examine the potential for dynamic hedging of mortality risk. Finally, we review a range of financial instruments (traded and over-the-counter) that could be used to hedge mortality and risk. Some of these, such as mortality swaps, already exist, while others anticipate future developments in the market.

Keywords: stochastic mortality models, short-rate models, market models, cohort
e®ect, SCOR market model, mortality-linked securities, mortality swaps, q-forwards.