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Semi-static hedging of variable annuities

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  • Bernard, Carole
  • Kwak, Minsuk

Abstract

This paper focuses on hedging financial risk in variable annuities with guarantees. We show that insurers should incorporate the specificity of the periodic payment of variable annuities fees to best hedge embedded guarantees and should focus on hedging the net liability. We develop a new hedging strategy based on semi-static hedging techniques, which takes into account the periodically collected fees, and confirm that it is more effective than delta-hedging with same rebalancing dates, as well as traditional semi-static hedging strategies that do not consider the specificity of the payments of fees in their optimization. It is also verified that short-selling or using put options as hedging instruments allows more effective hedging.

Suggested Citation

  • Bernard, Carole & Kwak, Minsuk, 2016. "Semi-static hedging of variable annuities," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 173-186.
    • Handle: RePEc:eee:insuma:v:67:y:2016:i:c:p:173-186
    DOI: 10.1016/j.insmatheco.2016.01.004
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    1. Alexandre Hocquard & Nicolas Papageorgiou & Bruno Remillard, 2015. "The payoff distribution model: an application to dynamic portfolio insurance," Quantitative Finance, Taylor & Francis Journals, vol. 15(2), pages 299-312, February.
    2. Bacinello, Anna Rita & Millossovich, Pietro & Olivieri, Annamaria & Pitacco, Ermanno, 2011. "Variable annuities: A unifying valuation approach," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 285-297.
    3. John Cotter & Jim Hanly, 2006. "Reevaluating hedging performance," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 26(7), pages 677-702, July.
    4. Mary Hardy, 2000. "Hedging and Reserving for Single-Premium Segregated Fund Contracts," North American Actuarial Journal, Taylor & Francis Journals, vol. 4(2), pages 63-74.
    5. Adam-Müller, Axel F.A. & Nolte, Ingmar, 2011. "Cross hedging under multiplicative basis risk," Journal of Banking & Finance, Elsevier, vol. 35(11), pages 2956-2964, November.
    6. T. F. Coleman & Y. Kim & Y. Li & M. Patron, 2007. "Robustly Hedging Variable Annuities With Guarantees Under Jump and Volatility Risks," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 74(2), pages 347-376, June.
    7. Milevsky, Moshe A. & Salisbury, Thomas S., 2006. "Financial valuation of guaranteed minimum withdrawal benefits," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 21-38, February.
    8. Coleman, Thomas F. & Li, Yuying & Patron, Maria-Cristina, 2006. "Hedging guarantees in variable annuities under both equity and interest rate risks," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 215-228, April.
    9. Kling, Alexander & Ruez, Frederik & Ruß, Jochen, 2011. "The Impact of Stochastic Volatility on Pricing, Hedging, and Hedge Efficiency of Withdrawal Benefit Guarantees in Variable Annuities," ASTIN Bulletin, Cambridge University Press, vol. 41(2), pages 511-545, November.
    10. 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.
    11. 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.
    12. Claymore Marshall & Mary Hardy & David Saunders, 2010. "Valuation of a Guaranteed Minimum Income Benefit," North American Actuarial Journal, Taylor & Francis Journals, vol. 14(1), pages 38-58.
    13. Bauer, Daniel & Kling, Alexander & Russ, Jochen, 2008. "A Universal Pricing Framework for Guaranteed Minimum Benefits in Variable Annuities1," ASTIN Bulletin, Cambridge University Press, vol. 38(2), pages 621-651, November.
    14. X. Lin & Ken Tan & Hailiang Yang, 2009. "Pricing Annuity Guarantees Under a Regime-Switching Model," North American Actuarial Journal, Taylor & Francis Journals, vol. 13(3), pages 316-332.
    15. Chen, Z. & Vetzal, K. & Forsyth, P.A., 2008. "The effect of modelling parameters on the value of GMWB guarantees," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 165-173, August.
    16. Min Dai & Yue Kuen Kwok & Jianping Zong, 2008. "Guaranteed Minimum Withdrawal Benefit In Variable Annuities," Mathematical Finance, Wiley Blackwell, vol. 18(4), pages 595-611, October.
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    Cited by:

    1. Bauer Jan, 2020. "Hedging of Variable Annuities under Basis Risk," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 14(2), pages 1-34, July.
    2. Jeon, Junkee & Kwak, Minsuk, 2018. "Optimal surrender strategies and valuations of path-dependent guarantees in variable annuities," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 93-109.
    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. Kang, Boda & Ziveyi, Jonathan, 2018. "Optimal surrender of guaranteed minimum maturity benefits under stochastic volatility and interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 43-56.
    5. Luca De Gennaro Aquino & Carole Bernard, 2019. "Semi-analytical prices for lookback and barrier options under the Heston model," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(2), pages 715-741, December.
    6. Ludovic Goudenege & Andrea Molent & Antonino Zanette, 2019. "Pricing and hedging GMWB in the Heston and in the Black–Scholes with stochastic interest rate models," Computational Management Science, Springer, vol. 16(1), pages 217-248, February.
    7. Andrea Molent, 2019. "Taxation of a GMWB Variable Annuity in a Stochastic Interest Rate Model," Papers 1901.11296, arXiv.org, revised May 2020.

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    More about this item

    Keywords

    Effective hedging; Variable annuities; Semi-static hedging; Periodic fees; Embedded guarantees;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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