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Longevity risk in portfolios of pension annuities


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  • Hári, Norbert
  • De Waegenaere, Anja
  • Melenberg, Bertrand
  • Nijman, Theo E.


We analyze the importance of longevity risk for the solvency of portfolios of pension annuities. We distinguish two types of mortality risk. Micro-longevity risk quantifies the risk related to uncertainty in the time of death if survival probabilities are known with certainty, while macro-longevity risk is due to uncertain future survival probabilities. We use a generalized two-factor Lee-Carter mortality model to produce forecasts of future mortality rates, and to assess the relative importance of micro- and macro-longevity risk for funding ratio uncertainty. The results show that if financial market risk is fully hedged so that uncertainty in future lifetime is the only source of uncertainty, pension funds are exposed to a substantial amount of risk. Systematic and non-systematic deviations from expected survival imply that, depending on the size of the portfolio, buffers that reduce the probability of underfunding to 2.5% at a 5-year horizon have to be of the order of magnitude of 7% to 8% of the initial value of the liabilities.

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Bibliographic Info

Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

Volume (Year): 42 (2008)
Issue (Month): 2 (April)
Pages: 505-519

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Handle: RePEc:eee:insuma:v:42:y:2008:i:2:p:505-519

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Cited by:
  1. Tomas Cipra, 2010. "Securitization of Longevity and Mortality Risk," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, Charles University Prague, Faculty of Social Sciences, vol. 60(6), pages 545-560, December.
  2. Anja De Waegenaere & Bertrand Melenberg & Ralph Stevens, 2010. "Longevity Risk," De Economist, Springer, Springer, vol. 158(2), pages 151-192, June.
  3. Stevens, R.S.P. & De Waegenaere, A.M.B. & Melenberg, B., 2011. "Longevity Risk and Natural Hedge Potential in Portfolios Of Life Insurance Products: The Effect of Investment Risk," Discussion Paper, Tilburg University, Center for Economic Research 2011-036, Tilburg University, Center for Economic Research.
  4. Alessandro Bucciol & Roel M.W.J. Beetsma, 2010. "Inter- and Intra-generational Consequences of Pension Buffer Policy under Demographic, Financial, and Economic Shocks," CESifo Economic Studies, CESifo, CESifo, vol. 56(3), pages 366-403, September.
  5. Helena Aro, 2013. "Systematic and non-systematic mortality risk in pension portfolios," Papers, 1307.8020,, revised Jul 2013.
  6. Katja Hanewald & Thomas Post & Helmut Gründl, 2009. "Stochastic Mortality, Macroeconomic Risks, and Life Insurer Solvency," SFB 649 Discussion Papers, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany SFB649DP2009-015, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  7. Petar Jevtic' & Luca Regis, 2014. "Assessing the solvency of insurance portfolios via a continuous time cohort model," Working Papers, IMT Institute for Advanced Studies Lucca 7/2014, IMT Institute for Advanced Studies Lucca, revised Jul 2014.
  8. Stevens, Ralph & De Waegenaere, Anja & Melenberg, Bertrand, 2010. "Longevity risk in pension annuities with exchange options: The effect of product design," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 46(1), pages 222-234, February.
  9. Cocco, João F. & Gomes, Francisco J., 2012. "Longevity risk, retirement savings, and financial innovation," Journal of Financial Economics, Elsevier, Elsevier, vol. 103(3), pages 507-529.
  10. Lin, Tzuling & Tzeng, Larry Y., 2010. "An additive stochastic model of mortality rates: An application to longevity risk in reserve evaluation," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 46(2), pages 423-435, April.
  11. Elisa Luciano & Luca Regis & Elena Vigna, 2012. "Natural delta gamma hedging of longevity and interest rate risk," ICER Working Papers - Applied Mathematics Series, ICER - International Centre for Economic Research 21-2011, ICER - International Centre for Economic Research.
  12. Yang, Sharon S. & Yue, Jack C. & Huang, Hong-Chih, 2010. "Modeling longevity risks using a principal component approach: A comparison with existing stochastic mortality models," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 46(1), pages 254-270, February.
  13. Mariarosaria Coppola & Valeria D'Amato, 2012. "Backtesting the solvency capital requirement for longevity risk," Journal of Risk Finance, Emerald Group Publishing, Emerald Group Publishing, vol. 13(4), pages 309-319.


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