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Pricing and hedging guaranteed annuity options via static option replication

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  • Pelsser, Antoon

Abstract

In this paper we derive a market value for Guaranteed Annuity Optionusing martingale modeling techniques. Furthermore, we show how to construct a static replicating portfolio of vanillainterest rate swaptions that replicates the Guaranteed Annuity Option. Finally, we illustrate with historical UK interest rate data from the period1980 until 2000 that the static replicating portfolio is extremely effective asa hedge against the interest rate risk involved in the GAO, that thestatic replicating portfolio is considerably cheaper than up-front reservingand also that the replicating portfolio provides a much better level ofprotection than an up-front reserve.
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  • Pelsser, Antoon, 2003. "Pricing and hedging guaranteed annuity options via static option replication," Insurance: Mathematics and Economics, Elsevier, vol. 33(2), pages 283-296, October.
    • Handle: RePEc:eee:insuma:v:33:y:2003:i:2:p:283-296
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    1. David Blake & Marco Morales & Enrico Biffis & Yijia Lin & Andreas Milidonis, 2017. "Special Edition: Longevity 10 – The Tenth International Longevity Risk and Capital Markets Solutions Conference," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(S1), pages 515-532, April.
    2. van Haastrecht, Alexander & Plat, Richard & Pelsser, Antoon, 2010. "Valuation of guaranteed annuity options using a stochastic volatility model for equity prices," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 266-277, December.
    3. 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.
    4. Jan Natolski & Ralf Werner, 2017. "Mathematical Analysis of Replication by Cash Flow Matching," Risks, MDPI, vol. 5(1), pages 1-15, February.
    5. Antje Mahayni & Erik Schlögl, 2003. "The Risk Management of Minimum Return Guarantees," Research Paper Series 102, Quantitative Finance Research Centre, University of Technology, Sydney.
    6. Matheus R Grasselli & Sebastiano Silla, 2009. "A policyholder's utility indifference valuation model for the guaranteed annuity option," Papers 0908.3196, arXiv.org.
    7. Dong, Bing & Xu, Wei & Sevic, Aleksandar & Sevic, Zeljko, 2020. "Efficient willow tree method for variable annuities valuation and risk management☆," International Review of Financial Analysis, Elsevier, vol. 68(C).
    8. Kleinow, Torsten, 2009. "Valuation and hedging of participating life-insurance policies under management discretion," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 78-87, February.
    9. Vikranth Lokeshwar & Vikram Bhardawaj & Shashi Jain, 2019. "Neural network for pricing and universal static hedging of contingent claims," Papers 1911.11362, arXiv.org.
    10. Yichen Han & Dongchen Li & Kun Fan & Jiaxin Wan & Luyan Li, 2024. "Valuation of a Mixture of GMIB and GMDB Variable Annuity," Mathematics, MDPI, vol. 12(3), pages 1-22, January.
    11. 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.
    12. Deelstra, Griselda & Rayée, Grégory, 2013. "Pricing Variable Annuity Guarantees in a local volatility framework," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 650-663.
    13. Thomas Poufinas, 2011. "On the pricing of single premium variable annuities with periodic fees and periodic cost of insurance using option pricing techniques," International Journal of Financial Markets and Derivatives, Inderscience Enterprises Ltd, vol. 2(3), pages 180-194.
    14. Deelstra, Griselda & Grasselli, Martino & Van Weverberg, Christopher, 2016. "The role of the dependence between mortality and interest rates when pricing Guaranteed Annuity Options," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 205-219.
    15. Cairns, Andrew J.G. & Blake, David & Dowd, Kevin, 2006. "Pricing Death: Frameworks for the Valuation and Securitization of Mortality Risk," ASTIN Bulletin, Cambridge University Press, vol. 36(1), pages 79-120, May.
    16. Ankush Agarwal & Christian-Oliver Ewald & Yongjie Wang, 2023. "Hedging longevity risk in defined contribution pension schemes," Computational Management Science, Springer, vol. 20(1), pages 1-34, December.
    17. Lokeshwar, Vikranth & Bharadwaj, Vikram & Jain, Shashi, 2022. "Explainable neural network for pricing and universal static hedging of contingent claims," Applied Mathematics and Computation, Elsevier, vol. 417(C).
    18. Carbonneau, Alexandre, 2021. "Deep hedging of long-term financial derivatives," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 327-340.
    19. Ballotta, Laura & Haberman, Steven, 2003. "Valuation of guaranteed annuity conversion options," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 87-108, August.
    20. Ballotta, Laura & Haberman, Steven, 2006. "The fair valuation problem of guaranteed annuity options: The stochastic mortality environment case," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 195-214, February.
    21. Eckhard Platen, 2009. "Real World Pricing of Long Term Contracts," Research Paper Series 262, Quantitative Finance Research Centre, University of Technology, Sydney.
    22. Thomas Post, 2009. "Individual Welfare Gains from Deferred Life-Annuities under Stochastic Lee-Carter Mortality," SFB 649 Discussion Papers SFB649DP2009-022, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    23. Schrager, David F., 2006. "Affine stochastic mortality," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 81-97, February.
    24. Lee, Yung-Tsung, 2015. "A Framework to Charge for Unit-Linked Contracts When Considering Guaranteed Risk," Asian Economic and Financial Review, Asian Economic and Social Society, vol. 5(3), pages 495-509, March.
    25. Vasilios N. Katsikis & Spyridon D. Mourtas, 2020. "ORPIT: A Matlab Toolbox for Option Replication and Portfolio Insurance in Incomplete Markets," Computational Economics, Springer;Society for Computational Economics, vol. 56(4), pages 711-721, December.

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    More about this item

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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