IDEAS home Printed from https://ideas.repec.org/a/cup/anacsi/v5y2011i02p211-230_00.html
   My bibliography  Save this article

A Natural Hedge for Equity Indexed Annuities

Author

Listed:
  • Bernard, Carole
  • Boyle, Phelim P.

Abstract

Equity linked products are popular in many countries. These contracts generally provide a guaranteed return combined with some participation in the market performance, often computed using a complicated formula. Hedging these contracts often presents a real challenge for insurers in particular during a financial crisis. In this paper, we explain how insurers can benefit from selling a pool of different contracts with different sensitivities to certain key variables to reduce risk exposure. We show how they can diversify their menu of policy designs to stabilize the market value of their liabilities against changes in the market volatility and against estimation error in the volatility parameter. We illustrate the methodology with specific examples of equity annuity contracts with opposite sensitivities to vega risk.

Suggested Citation

  • Bernard, Carole & Boyle, Phelim P., 2011. "A Natural Hedge for Equity Indexed Annuities," Annals of Actuarial Science, Cambridge University Press, vol. 5(2), pages 211-230, September.
    • Handle: RePEc:cup:anacsi:v:5:y:2011:i:02:p:211-230_00
    as

    Download full text from publisher

    File URL: https://www.cambridge.org/core/product/identifier/S1748499511000066/type/journal_article
    File Function: link to article abstract page
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. John Piggott & Emiliano A. Valdez & Bettina Detzel, 2005. "The Simple Analytics of a Pooled Annuity Fund," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 72(3), pages 497-520, September.
    2. Guillaume Plantin & Haresh Sapra & Hyun Song Shin, 2004. "Fair Value Reporting Standards and Market Volatility," Sciences Po publications info:hdl:2441/70ur20flu79, Sciences Po.
    3. Anna Rita Bacinello, 2003. "Pricing Guaranteed Life Insurance Participating Policies with Annual Premiums and Surrender Option," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(3), pages 1-17.
    4. Carole Bernard & Olivier Le Courtois & François Quittard-Pinon, 2006. "Development and Pricing of a New Participating Contract," North American Actuarial Journal, Taylor & Francis Journals, vol. 10(4), pages 179-195.
    5. repec:hal:spmain:info:hdl:2441/70ur20flu79u1at4a0q027ojpr is not listed on IDEAS
    6. Bacinello, Anna Rita, 2001. "Fair Pricing of Life Insurance Participating Policies with a Minimum Interest Rate Guaranteed," ASTIN Bulletin, Cambridge University Press, vol. 31(2), pages 275-297, November.
    7. Bernard, Carole & Le Courtois, Olivier & Quittard-Pinon, Francois, 2005. "Market value of life insurance contracts under stochastic interest rates and default risk," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 499-516, June.
    8. Ballotta, Laura, 2005. "A Lévy process-based framework for the fair valuation of participating life insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 37(2), pages 173-196, October.
    9. Barbarin, Jerome & Devolder, Pierre, 2005. "Risk measure and fair valuation of an investment guarantee in life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 37(2), pages 297-323, October.
    10. Aase Nielsen, J. & Sandmann, Klaus, 1995. "Equity-linked life insurance: A model with stochastic interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 16(3), pages 225-253, July.
    11. Grosen, Anders & Lochte Jorgensen, Peter, 2000. "Fair valuation of life insurance liabilities: The impact of interest rate guarantees, surrender options, and bonus policies," Insurance: Mathematics and Economics, Elsevier, vol. 26(1), pages 37-57, February.
    12. Boyle, Phelim & Hardy, Mary, 2003. "Guaranteed Annuity Options," ASTIN Bulletin, Cambridge University Press, vol. 33(2), pages 125-152, November.
    13. Bacinello, Anna Rita, 2005. "Endogenous model of surrender conditions in equity-linked life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 37(2), pages 270-296, October.
    14. Brennan, Michael J. & Schwartz, Eduardo S., 1976. "The pricing of equity-linked life insurance policies with an asset value guarantee," Journal of Financial Economics, Elsevier, vol. 3(3), pages 195-213, June.
    15. Tanskanen, Antti Juho & Lukkarinen, Jani, 2003. "Fair valuation of path-dependent participating life insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 595-609, December.
    16. Samuel Cox & Yijia Lin, 2007. "Natural Hedging of Life and Annuity Mortality Risks," North American Actuarial Journal, Taylor & Francis Journals, vol. 11(3), pages 1-15.
    17. Boyle, Phelim P. & Hardy, Mary R., 1997. "Reserving for maturity guarantees: Two approaches," Insurance: Mathematics and Economics, Elsevier, vol. 21(2), pages 113-127, November.
    18. Grosen, Anders & Løchte Jørgensen, Peter, 2001. "Life Insurance Liabilities at Market Value," Finance Working Papers 01-4, University of Aarhus, Aarhus School of Business, Department of Business Studies.
    19. Laura Ballotta & Steven Haberman & Nan Wang, 2006. "Guarantees in With‐Profit and Unitized With‐Profit Life Insurance Contracts: Fair Valuation Problem in Presence of the Default Option," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(1), pages 97-121, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kirkby, J. Lars & Nguyen, Duy, 2021. "Equity-linked Guaranteed Minimum Death Benefits with dollar cost averaging," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 408-428.
    2. Cui, Zhenyu & Kirkby, J. Lars & Nguyen, Duy, 2017. "Equity-linked annuity pricing with cliquet-style guarantees in regime-switching and stochastic volatility models with jumps," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 46-62.
    3. Hanna, Vanessa & Hieber, Peter & Devolder, Pierre, 2021. "Mixed participating and unit-linked life insurance contracts: design, pricing and optimal strategy," LIDAM Discussion Papers ISBA 2021010, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Eckhard Platen, 2009. "Real World Pricing of Long Term Contracts," Research Paper Series 262, Quantitative Finance Research Centre, University of Technology, Sydney.
    2. Kevin Fergusson & Eckhard Platen, 2013. "Real World Pricing of Long Term Cash-Linked Annuities and Equity-Linked Annuities with Cash-Linked Guarantees," Research Paper Series 338, Quantitative Finance Research Centre, University of Technology, Sydney.
    3. Olivier Le Courtois & François Quittard-Pinon & Xiaoshan Su, 2020. "Pricing and hedging defaultable participating contracts with regime switching and jump risk," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 303-339, June.
    4. Gerstner, Thomas & Griebel, Michael & Holtz, Markus & Goschnick, Ralf & Haep, Marcus, 2008. "A general asset-liability management model for the efficient simulation of portfolios of life insurance policies," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 704-716, April.
    5. Bernard Carole & Le Courtois Olivier, 2012. "Asset Risk Management of Participating Contracts," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 6(2), pages 1-23, June.
    6. Olivier Le Courtois & François Quittard-Pinon, 2008. "Fair Valuation of Participating Life Insurance Contracts with Jump Risk," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 33(2), pages 106-136, December.
    7. Gatzert, Nadine, 2008. "Asset management and surplus distribution strategies in life insurance: An examination with respect to risk pricing and risk measurement," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 839-849, April.
    8. Kleinow, Torsten & Willder, Mark, 2007. "The effect of management discretion on hedging and fair valuation of participating policies with maturity guarantees," Insurance: Mathematics and Economics, Elsevier, vol. 40(3), pages 445-458, May.
    9. Laura Ballotta, 2009. "Pricing and capital requirements for with profit contracts: modelling considerations," Quantitative Finance, Taylor & Francis Journals, vol. 9(7), pages 803-817.
    10. Ballotta, Laura, 2005. "A Lévy process-based framework for the fair valuation of participating life insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 37(2), pages 173-196, October.
    11. Barbarin, Jerome & Devolder, Pierre, 2005. "Risk measure and fair valuation of an investment guarantee in life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 37(2), pages 297-323, October.
    12. Zemp, Alexandra, 2011. "Risk comparison of different bonus distribution approaches in participating life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 49(2), pages 249-264, September.
    13. Nadine Gatzert & Hato Schmeiser, 2008. "Assessing the Risk Potential of Premium Payment Options in Participating Life Insurance Contracts," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 75(3), pages 691-712, September.
    14. Schmeiser, H. & Wagner, J., 2011. "A joint valuation of premium payment and surrender options in participating life insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 580-596.
    15. An Chen & Xia Su, 2009. "Knightian uncertainty and insurance regulation decision," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 32(1), pages 13-33, May.
    16. Thomas Poufinas, 2015. "On the pricing of regular premium variable annuities using options," International Journal of Financial Markets and Derivatives, Inderscience Enterprises Ltd, vol. 4(1), pages 54-77.
    17. Gerstner, Thomas & Griebel, Michael & Holtz, Markus, 2009. "Efficient deterministic numerical simulation of stochastic asset-liability management models in life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 434-446, June.
    18. Mahayni, Antje & Schlögl, Erik, 2003. "The Risk Management of Minimum Return Guarantees," Bonn Econ Discussion Papers 18/2003, University of Bonn, Bonn Graduate School of Economics (BGSE).
    19. Gan, Guojun, 2013. "Application of data clustering and machine learning in variable annuity valuation," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 795-801.
    20. Kassberger, Stefan & Kiesel, Rüdiger & Liebmann, Thomas, 2008. "Fair valuation of insurance contracts under Lévy process specifications," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 419-433, February.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cup:anacsi:v:5:y:2011:i:02:p:211-230_00. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Kirk Stebbing (email available below). General contact details of provider: https://www.cambridge.org/aas .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.