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Immunization and Hedging of Post Retirement Income Annuity Products

Author

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  • Changyu Liu

    (CEPAR and School of Risk and Actuarial Studies, UNSW Business School, University of New South Wales, 2052 Sydney, Australia)

  • Michael Sherris

    (CEPAR and School of Risk and Actuarial Studies, UNSW Business School, University of New South Wales, 2052 Sydney, Australia)

Abstract

Designing post retirement benefits requires access to appropriate investment instruments to manage the interest rate and longevity risks. Post retirement benefits are increasingly taken as a form of income benefit, either as a pension or an annuity. Pension funds and life insurers offer annuities generating long term liabilities linked to longevity. Risk management of life annuity portfolios for interest rate risks is well developed but the incorporation of longevity risk has received limited attention. We develop an immunization approach and a delta-gamma based hedging approach to manage the risks of adverse portfolio surplus using stochastic models for mortality and interest rates. We compare and assess the immunization and hedge effectiveness of fixed-income coupon bonds, annuity bonds, as well as longevity bonds, using simulations of the portfolio surplus for an annuity portfolio and a range of risk measures including value-at-risk. We show how fixed-income annuity bonds can more effectively match cash flows and provide additional hedge effectiveness over coupon bonds. Longevity bonds, including deferred longevity bonds, reduce risk significantly compared to coupon and annuity bonds, reflecting the long duration of the typical life annuity and the exposure to longevity risk. Longevity bonds are shown to be effective in immunizing surplus over short and long horizons. Delta gamma hedging is generally only effective over short horizons. The results of the paper have implications for how providers of post retirement income benefit streams can manage risks in demanding conditions where innovation in investment markets can support new products and increase the product range.

Suggested Citation

  • Changyu Liu & Michael Sherris, 2017. "Immunization and Hedging of Post Retirement Income Annuity Products," Risks, MDPI, vol. 5(1), pages 1-29, March.
    • Handle: RePEc:gam:jrisks:v:5:y:2017:i:1:p:19-:d:93259
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    References listed on IDEAS

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    1. Lin, Tzuling & Tsai, Cary Chi-Liang, 2013. "On the mortality/longevity risk hedging with mortality immunization," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 580-596.
    2. S. J. Koopman & J. Durbin, 2000. "Fast Filtering and Smoothing for Multivariate State Space Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(3), pages 281-296, May.
    3. Blackburn, Craig & Sherris, Michael, 2013. "Consistent dynamic affine mortality models for longevity risk applications," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 64-73.
    4. Rogers, L. C. G. & Stummer, Wolfgang, 2000. "Consistent fitting of one-factor models to interest rate data," Insurance: Mathematics and Economics, Elsevier, vol. 27(1), pages 45-63, August.
    5. Andy Wong & Michael Sherris & Ralph Stevens, 2017. "Natural Hedging Strategies for Life Insurers: Impact of Product Design and Risk Measure," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(1), pages 153-175, March.
    6. Fisher, Lawrence & Weil, Roman L, 1971. "Coping with the Risk of Interest-Rate Fluctuations: Returns to Bondholders from Naive and Optimal Strategies," The Journal of Business, University of Chicago Press, vol. 44(4), pages 408-431, October.
    7. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    8. Schrager, David F., 2006. "Affine stochastic mortality," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 81-97, February.
    9. Menoncin, Francesco, 2008. "The role of longevity bonds in optimal portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 343-358, February.
    10. Tsai, Cary Chi-Liang & Chung, San-Lin, 2013. "Actuarial applications of the linear hazard transform in mortality immunization," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 48-63.
    11. 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.
    12. Shiu, Elias S. W., 1987. "On the Fisher-Weil immunization theorem," Insurance: Mathematics and Economics, Elsevier, vol. 6(4), pages 259-266, November.
    13. Biffis, Enrico, 2005. "Affine processes for dynamic mortality and actuarial valuations," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 443-468, December.
    14. Luciano, Elisa & Regis, Luca & Vigna, Elena, 2012. "Delta–Gamma hedging of mortality and interest rate risk," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 402-412.
    15. Shiu, Elias S. W., 1988. "Immunization of multiple liabilities," Insurance: Mathematics and Economics, Elsevier, vol. 7(4), pages 219-224, December.
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    Cited by:

    1. Cláudia Simões & Luís Oliveira & Jorge M. Bravo, 2021. "Immunization Strategies for Funding Multiple Inflation-Linked Retirement Income Benefits," Risks, MDPI, vol. 9(4), pages 1-28, March.
    2. Joseba Iñaki De La Peña & Iván Iturricastillo & Rafael Moreno & Francisco Román & Eduardo Trigo, 2021. "Towards an immunization perfect model?," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(1), pages 1181-1196, January.

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