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Longevity risk management for life and variable annuities: The effectiveness of static hedging using longevity bonds and derivatives

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  • Ngai, Andrew
  • Sherris, Michael

Abstract

For many years, the longevity risk of individuals has been underestimated, as survival probabilities have improved across the developed world. The uncertainty and volatility of future longevity has posed significant risk issues for both individuals and product providers of annuities and pensions. This paper investigates the effectiveness of static hedging strategies for longevity risk management using longevity bonds and derivatives (q-forwards) for the retail products: life annuity, deferred life annuity, indexed life annuity, and variable annuity with guaranteed lifetime benefits. Improved market and mortality models are developed for the underlying risks in annuities. The market model is a regime-switching vector error correction model for GDP, inflation, interest rates, and share prices. The mortality model is a discrete-time logit model for mortality rates with age dependence. Models were estimated using Australian data. The basis risk between annuitant portfolios and population mortality was based on UK experience. Results show that static hedging using q-forwards or longevity bonds reduces the longevity risk substantially for life annuities, but significantly less for deferred annuities. For inflation-indexed annuities, static hedging of longevity is less effective because of the inflation risk. Variable annuities provide limited longevity protection compared to life annuities and indexed annuities, and as a result longevity risk hedging adds little value for these products.

Suggested Citation

  • Ngai, Andrew & Sherris, Michael, 2011. "Longevity risk management for life and variable annuities: The effectiveness of static hedging using longevity bonds and derivatives," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 100-114, July.
  • Handle: RePEc:eee:insuma:v:49:y:2011:i:1:p:100-114
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    References listed on IDEAS

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    Cited by:

    1. Shao, Adam W. & Hanewald, Katja & Sherris, Michael, 2015. "Reverse mortgage pricing and risk analysis allowing for idiosyncratic house price risk and longevity risk," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 76-90.
    2. Anastasia Novokreshchenova, 2016. "Predicting Human Mortality: Quantitative Evaluation of Four Stochastic Models," Risks, MDPI, Open Access Journal, vol. 4(4), pages 1-28, December.
    3. Li, Jackie & Haberman, Steven, 2015. "On the effectiveness of natural hedging for insurance companies and pension plans," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 286-297.
    4. Huang, H. & Milevsky, M.A. & Salisbury, T.S., 2014. "Optimal initiation of a GLWB in a variable annuity: No Arbitrage approach," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 102-111.
    5. Meyricke, Ramona & Sherris, Michael, 2014. "Longevity risk, cost of capital and hedging for life insurers under Solvency II," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 147-155.
    6. Liu, Yanxin & Li, Johnny Siu-Hang, 2016. "It’s all in the hidden states: A longevity hedging strategy with an explicit measure of population basis risk," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 301-319.
    7. Petar Jevtic' & Luca Regis, 2014. "Assessing the solvency of insurance portfolios via a continuous time cohort model," Working Papers 7/2014, IMT Institute for Advanced Studies Lucca, revised Jul 2014.
    8. repec:bla:jrinsu:v:84:y:2017:i:s1:p:417-437 is not listed on IDEAS
    9. Fung, Man Chung & Ignatieva, Katja & Sherris, Michael, 2014. "Systematic mortality risk: An analysis of guaranteed lifetime withdrawal benefits in variable annuities," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 103-115.
    10. Hanewald, Katja & Piggott, John & Sherris, Michael, 2013. "Individual post-retirement longevity risk management under systematic mortality risk," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 87-97.
    11. Jevtić, Petar & Regis, Luca, 2015. "Assessing the solvency of insurance portfolios via a continuous-time cohort model," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 36-47.
    12. repec:bla:jrinsu:v:84:y:2017:i:1:p:153-175 is not listed on IDEAS
    13. repec:gam:jrisks:v:6:y:2018:i:1:p:10-:d:131400 is not listed on IDEAS
    14. Boonen, Tim J. & De Waegenaere, Anja & Norde, Henk, 2017. "Redistribution of longevity risk: The effect of heterogeneous mortality beliefs," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 175-188.
    15. Yahia Salhi & Pierre-Emmanuel Thérond & Julien Tomas, 2016. "A Credibility Approach of the Makeham Mortality Law," Post-Print hal-01232683, HAL.
    16. Bernard, Carole & Kwak, Minsuk, 2016. "Semi-static hedging of variable annuities," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 173-186.
    17. Forsyth, Peter & Vetzal, Kenneth, 2014. "An optimal stochastic control framework for determining the cost of hedging of variable annuities," Journal of Economic Dynamics and Control, Elsevier, vol. 44(C), pages 29-53.
    18. Parsiad Azimzadeh & Peter A. Forsyth, 2015. "The existence of optimal bang-bang controls for GMxB contracts," Papers 1502.05743, arXiv.org, revised Nov 2015.
    19. repec:hal:wpaper:hal-01232683 is not listed on IDEAS
    20. Clemente De Rosa & Elisa Luciano & Luca Regis, 2015. "Basis risk in static versus dynamic longevity-risk hedging," Carlo Alberto Notebooks 425, Collegio Carlo Alberto, revised Oct 2015.
    21. Helena Chuliá & Montserrat Guillén & Jorge M. Uribe, 2015. "Mortality and Longevity Risks in the United Kingdom: Dynamic Factor Models and Copula-Functions," Working Papers 2015-03, Universitat de Barcelona, UB Riskcenter.
    22. Man Chung Fung & Katja Ignatieva & Michael Sherris, 2015. "Managing Systematic Mortality Risk in Life Annuities: An Application of Longevity Derivatives," Papers 1508.00090, arXiv.org.
    23. Clemente De Rosa & Elisa Luciano & Luca Regis, 2015. "Static versus dynamic longevity-risk hedging," Carlo Alberto Notebooks 403, Collegio Carlo Alberto.
    24. Chao Qiao & Michael Sherris, 2013. "Managing Systematic Mortality Risk With Group Self-Pooling and Annuitization Schemes," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(4), pages 949-974, December.

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