Mortality-Dependent Financial Risk Measures

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

This paper uses a recently developed two-factor stochastic mortality
model to estimate financial risk measures for four illustrative types of
mortality-dependent financial position: investments in zero-coupon
longevity bonds; investments in longevity bonds that pay annual
survivor-dependent coupons; and two examples of an insurer’s annuity
book that are each hedged by a longevity bond, one based on the annuity
book and hedge having the same reference cohort, and the other not. The
risk measures estimated are the value-at-risk, the expected shortfall and a
spectral risk measure based on an exponential risk-aversion function.
Results are reported on a model calibrated on data provided by the UK
Government Actuary’s Department, both with and without underlying parameter
uncertainty. © 2005 Elsevier B.V. All rights reserved.

Keywords: Mortality risk; Longevity bonds; Value-at-risk; Coherent risk
measures; Spectral risk measures

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