Abstract
Pension plan sponsors and annuity providers can offload their longevity risk exposures by trading securities that are linked to broad-based mortality indexes. However, a hedge constructed in this way is subject to population basis risk, arising from the difference in mortality improvements between the hedger’s population and the reference population to which the security is linked. To address this problem, which is believed to be a major obstacle to market development, in this paper we contribute a graphical population basis risk metric. The graphical metric allows market participants to not only visually evaluate the extent of population basis risk, but also determine the most appropriate reference population. We illustrate this concept with a hypothetical example.
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Notes
Life and Longevity Markets Association (LLMA) (2012).
Stevens et al. (2011). The minimal required buffer refers to the minimum asset value (in excess of the best estimate value of the liabilities) such that the probability that the insurer or pension fund will be able to pay all future liabilities is sufficiently high.
Static hedging is more realistic, because dynamic hedging requires liquid longevity-linked securities that are not yet available in the current market for longevity risk transfers. See Fung et al. (2014).
As a matter of fact, the LLMA (www.llma.org) provides mortality indexes for these four national populations. Derivative securities can be written on LLMA's mortality indexes.
The approximation is exact if the force of mortality between two integer ages is constant.
See Gnanadesikan and Kettenring (1972) for further information about Mahalanobis distances.
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Acknowledgements
This work is supported by research grants from the Global Risk Institute, the Natural Science and Engineering Research Council of Canada, the Society of Actuaries Center of Actuarial Excellence Program, and the Research Grants Council of the Hong Kong Special Administrative Region (General Research Fund Project No. CUHK 440812H).
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Chan, WS., Li, JH., Zhou, K. et al. Towards a Large and Liquid Longevity Market: A Graphical Population Basis Risk Metric. Geneva Pap Risk Insur Issues Pract 41, 118–127 (2016). https://doi.org/10.1057/gpp.2015.9
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DOI: https://doi.org/10.1057/gpp.2015.9