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Integrating Financial and Demographic Longevity Risk Models: An Australian Model for Financial

Samuel Wills and Michael Sherris

Since its introduction, the Lee Carter model has been widely adopted as a means
of modelling the distribution of projected mortality rates. Increasingly attention is
being placed on alternative models and, importantly in the financial and actuarial
literature, on models suited to risk management and pricing. Financial economic
approaches based on term structure models provide a framework for embedding
longevity models into a pricing and risk management framework. They can include
traditional actuarial models for the force of mortality as well as multiple risk factor
models. The paper develops a stochastic longevity model suitable for financial
pricing and risk management applications based on Australian population mortality
rates from 1971-2004 for ages 50-99. The model allows for expected changes aris-
ing from age and cohort erects and includes multiple stochastic risk factors. The
model captures age and time e®ects and allows for age dependence in the stochastic
factors driving longevity improvements. The model provides a good fit to historical
data capturing the stochastic trends in mortality improvement at di®erent ages and
across time as well as the multivariate dependence structure across ages.

Keywords: longevity, mortality, pricing, risk management