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

Hunt, A. & Blake, D. ORCID: 0000-0002-2453-2090 (2020). Forward Mortality Rates in Discrete Time I: Calibration and Securities Pricing. North American Actuarial Journal, 25(S1), S482-S507. doi: 10.1080/10920277.2019.1649159


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), though 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.

Publication Type: Article
Additional Information: This is an Accepted Manuscript version of the following article, accepted for publication in North American Actuarial Journal. Andrew Hunt & David Blake (2021) Forward Mortality Rates in Discrete Time I: Calibration and Securities Pricing, North American Actuarial Journal, 25:sup1, S482-S507. It is deposited under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License (, which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited, and is not altered, transformed, or built upon in any way.
Subjects: G Geography. Anthropology. Recreation > GN Anthropology
H Social Sciences > HF Commerce
Departments: Bayes Business School > Finance
Text - Accepted Version
Available under License Creative Commons Attribution Non-commercial.

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