Forward Mortality Rates in Discrete Time I: Calibration and Securities Pricing

Pensions Institute Discussion Paper, PI-1511, September 2015

57 Pages Posted: 16 Mar 2020

See all articles by Andrew Hunt

Andrew Hunt

City University London - Sir John Cass Business School

David P. Blake

City, University of London

Date Written: September 1, 2015

Abstract

Many users of mortality models are interested in using them to place values on longevity-linked liabilities and securities. Modern regulatory regimes require that the values of liabilities and reserves are consistent with market prices (if available), whilst the gradual emergence of a traded market in longevity risk needs methods for pricing new types of longevity-linked securities quickly and efficiently. In this study, we develop a new forward mortality framework to enable the efficient pricing of longevity-linked liabilities and securities in a market-consistent fashion. This approach starts from the historical data of the observed mortality rates, i.e., the force of mortality. Building on the dynamics of age/period/cohort models of the observed force of mortality, we develop models of forward mortality rates and then use a change of measure to incorporate whatever market information is available. The resulting forward mortality rates are then used to value a number of different longevity-linked securities, such as q-forwards, s-forwards and longevity swaps.

Keywords: mortality modelling, age/period/cohort models, forward mortality rates, Esscher transform, longevity-linked securities

JEL Classification: G12

Suggested Citation

Hunt, Andrew and Blake, David P., Forward Mortality Rates in Discrete Time I: Calibration and Securities Pricing (September 1, 2015). Pensions Institute Discussion Paper, PI-1511, September 2015, Available at SSRN: https://ssrn.com/abstract=3552220 or http://dx.doi.org/10.2139/ssrn.3552220

Andrew Hunt

City University London - Sir John Cass Business School ( email )

106 Bunhill Row
London, EC1Y 8TZ
United Kingdom

David P. Blake (Contact Author)

City, University of London ( email )

106 Bunhill Row
London, EC1Y 8TZX
Great Britain
+44 (0) 20-7040-8600 (Phone)
+44 (0) 20-7040-8881 (Fax)

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