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The determinants of mortality heterogeneity and implications for pricing annuities

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  • Meyricke, Ramona
  • Sherris, Michael

Abstract

Standard annuities are offered at one price to all individuals of the same age and gender. Individual mortality heterogeneity exposes insurers to adverse selection since only relatively healthy lives are expected to purchase annuities. As a result standard annuities are priced assuming above-average longevity, making them expensive for many individuals. In contrast underwritten annuity prices reflect individual risk factors based on underwriting information, as well as age and gender. While underwriting reduces heterogeneity, mortality risk still varies within each risk class due to unobservable individual risk factors, referred to as frailty. This paper quantifies the impact of heterogeneity due to underwriting factors and frailty on annuity values. Heterogeneity is quantified by fitting Generalized Linear Mixed Models to longitudinal data for a large sample of US males. The results show that heterogeneity remains after underwriting and that frailty significantly impacts the fair value of both standard and underwritten annuities. We develop a method to adjust annuity prices to allow for frailty.

Suggested Citation

  • Meyricke, Ramona & Sherris, Michael, 2013. "The determinants of mortality heterogeneity and implications for pricing annuities," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 379-387.
    • Handle: RePEc:eee:insuma:v:53:y:2013:i:2:p:379-387
    DOI: 10.1016/j.insmatheco.2013.06.002
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    References listed on IDEAS

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    1. Steinorth, Petra, 2012. "The demand for enhanced annuities," Journal of Public Economics, Elsevier, vol. 96(11), pages 973-980.
    2. Michael Rothschild & Joseph Stiglitz, 1976. "Equilibrium in Competitive Insurance Markets: An Essay on the Economics of Imperfect Information," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 90(4), pages 629-649.
    3. Olivia Mitchell & David McCarthy, 2002. "Estimating International Adverse Selection in Annuities," North American Actuarial Journal, Taylor & Francis Journals, vol. 6(4), pages 38-54.
    4. Su, Shu & Sherris, Michael, 2012. "Heterogeneity of Australian population mortality and implications for a viable life annuity market," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 322-332.
    5. Robert Brown & Joanne McDaid, 2003. "Factors Affecting Retirement Mortality," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(2), pages 24-43.
    6. Kwon, Hyuk-Sung & Jones, Bruce L., 2006. "The impact of the determinants of mortality on life insurance and annuities," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 271-288, April.
    7. X. Lin & Xiaoming Liu, 2007. "Markov Aging Process and Phase-Type Law of Mortality," North American Actuarial Journal, Taylor & Francis Journals, vol. 11(4), pages 92-109.
    8. Antonio, Katrien & Beirlant, Jan, 2007. "Actuarial statistics with generalized linear mixed models," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 58-76, January.
    9. Pitacco, Ermanno, 2004. "Survival models in a dynamic context: a survey," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 279-298, October.
    10. James Vaupel & Kenneth Manton & Eric Stallard, 1979. "The impact of heterogeneity in individual frailty on the dynamics of mortality," Demography, Springer;Population Association of America (PAA), vol. 16(3), pages 439-454, August.
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    Cited by:

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    More about this item

    Keywords

    Mortality heterogeneity; Frailty modelling; Annuity pricing; Longitudinal data; Generalized linear mixed models;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • G23 - Financial Economics - - Financial Institutions and Services - - - Non-bank Financial Institutions; Financial Instruments; Institutional Investors
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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