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PRICING LONGEVITY-LINKED SECURITIES IN THE PRESENCE OF MORTALITY TREND CHANGES

Published online by Cambridge University Press:  10 March 2021

Arne Freimann
Arne Freimann*
Affiliation:
Institute for Finance and Actuarial Sciences (ifa) Lise-Meitner-Str. 14, 89081Ulm, Germany Institute of Insurance Science, University of Ulm Helmholtzstr. 20, 89069 Ulm, Germany E-Mail: a.freimann@ifa-ulm.de
*
E-Mail: a.freimann@ifa-ulm.de
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Abstract

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Even though the trend in mortality improvements has experienced several permanent changes in the past, the uncertainty regarding future mortality trends is often left unmodeled when pricing longevity-linked securities. In this paper, we present a stochastic modeling framework for the valuation of longevity-linked securities which explicitly considers the risk of random future changes in the long-term mortality trend. We construct a set of meaningful probability distortions which imply equivalent risk-adjusted pricing measures under which the basic model structure is preserved. Inspired by risk-based capital requirements for (re)insurers, we also establish a cost-of-capital pricing approach which then serves as the appropriate reference framework for finding a reasonable range for the market price of longevity risk. In a numerical application, we demonstrate that our model produces plausible risk loadings and show that a greater proportion of the risk loading is allocated to longer maturities when the risk of random future mortality trend changes is adequately modeled.

Keywords

Longevity risklongevity derivativesstochastic mortalitymortality trend processesG13G22
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 51 , Issue 2 , May 2021 , pp. 411 - 447
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© 2021 by Astin Bulletin. All rights reserved

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