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Analyzing the interest rate risk of equity-indexed annuities via scenario matrices

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  • Günther, Sascha
  • Hieber, Peter

Abstract

The financial return of equity-indexed annuities depends on an underlying fund or investment portfolio complemented by an investment guarantee. We discuss a so-called cliquet-style or ratchet-type guarantee granting a minimum annual return. Its path-dependent payoff complicates valuation and risk management, especially if interest rates are modelled stochastically. We develop a novel scenario-matrix (SM) method. In the example of a Vasicek-Black-Scholes model, we derive closed-form expressions for the value and moment-generating function of the final payoff in terms of the scenario matrix. This allows efficient evaluation of values and various risk measures, avoiding Monte-Carlo simulation or numerical Fourier inversion. In numerical tests, this procedure proves to converge quickly and outperforms the existing approaches in the literature in terms of computation time and accuracy.

Suggested Citation

  • Günther, Sascha & Hieber, Peter, 2024. "Analyzing the interest rate risk of equity-indexed annuities via scenario matrices," Insurance: Mathematics and Economics, Elsevier, vol. 114(C), pages 15-28.
    • Handle: RePEc:eee:insuma:v:114:y:2024:i:c:p:15-28
    DOI: 10.1016/j.insmatheco.2023.10.003
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    1. Kijima, Masaaki & Wong, Tony, 2007. "Pricing of Ratchet equity-indexed annuities under stochastic interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 41(3), pages 317-338, November.
    2. X. Sheldon Lin & Ken Seng Tan, 2003. "Valuation of Equity-Indexed Annuities Under Stochastic Interest Rates," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(4), pages 72-91.
    3. Fan, Kun & Shen, Yang & Siu, Tak Kuen & Wang, Rongming, 2015. "Pricing annuity guarantees under a double regime-switching model," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 62-78.
    4. Ignatieva, Katja & Song, Andrew & Ziveyi, Jonathan, 2016. "Pricing and hedging of guaranteed minimum benefits under regime-switching and stochastic mortality," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 286-300.
    5. Zaglauer, Katharina & Bauer, Daniel, 2008. "Risk-neutral valuation of participating life insurance contracts in a stochastic interest rate environment," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 29-40, August.
    6. 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.
    7. Miltersen, Kristian R. & Persson, Svein-Arne, 1999. "Pricing rate of return guarantees in a Heath-Jarrow-Morton framework," Insurance: Mathematics and Economics, Elsevier, vol. 25(3), pages 307-325, December.
    8. Eric Briys & François De Varenne, 1994. "Life Insurance in a Contingent Claim Framework: Pricing and Regulatory Implications," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 19(1), pages 53-72, June.
    9. 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.
    10. Deelstra, Griselda & Hieber, Peter, 2023. "Randomization and the valuation of guaranteed minimum death benefits," European Journal of Operational Research, Elsevier, vol. 309(3), pages 1218-1236.
    11. 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.
    12. Kristian R. Miltersen & Svein-arne Persson, 2003. "Guaranteed Investment Contracts: Distributed and Undistributed Excess Return," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2003(4), pages 257-279.
    13. Peter Hieber & Jan Natolski & Ralf Werner, 2019. "Fair valuation of cliquet-style return guarantees in (homogeneous and) heterogeneous life insurance portfolios," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2019(6), pages 478-507, July.
    14. 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.
    15. 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.
    16. 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.
    17. Kirkby, J. Lars, 2023. "Hybrid equity swap, cap, and floor pricing under stochastic interest by Markov chain approximation," European Journal of Operational Research, Elsevier, vol. 305(2), pages 961-978.
    18. Hieber, Peter, 2017. "Cliquet-style return guarantees in a regime switching Lévy model," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 138-147.
    19. 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.
    20. Li, Yuying & Forsyth, Peter A., 2019. "A data-driven neural network approach to optimal asset allocation for target based defined contribution pension plans," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 189-204.
    21. Chia Chun Lo & Konstantinos Skindilias, 2014. "An Improved Markov Chain Approximation Methodology: Derivatives Pricing And Model Calibration," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(07), pages 1-22.
    22. Chen, An & Hieber, Peter, 2016. "Optimal Asset Allocation In Life Insurance: The Impact Of Regulation," ASTIN Bulletin, Cambridge University Press, vol. 46(3), pages 605-626, September.
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    More about this item

    Keywords

    Equity-indexed annuities; Cliquet-style guarantees; Vasicek model; Stochastic interest rates;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • G23 - Financial Economics - - Financial Institutions and Services - - - Non-bank Financial Institutions; Financial Instruments; Institutional Investors
    • G52 - Financial Economics - - Household Finance - - - Insurance

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