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Pricing and hedging of guaranteed minimum benefits under regime-switching and stochastic mortality

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  • Ignatieva, Katja
  • Song, Andrew
  • Ziveyi, Jonathan

Abstract

This paper presents a novel framework for pricing and hedging of the Guaranteed Minimum Benefits (GMBs) embedded in variable annuity (VA) contracts whose underlying mutual fund dynamics evolve under the influence of the regime-switching model. Semi-closed form solutions for prices and Greeks (i.e. sensitivities of prices with respect to model parameters) of various GMBs under stochastic mortality are derived. Pricing and hedging is performed using an accurate, fast and efficient Fourier Space Time-stepping (FST) algorithm. The mortality component of the model is calibrated to the Australian male population. Sensitivity analysis is performed with respect to various parameters including guarantee levels, time to maturity, interest rates and volatilities. The hedge effectiveness is assessed by comparing profit-and-loss distributions for an unhedged, statically and semi-statically hedged portfolios. The results provide a comprehensive analysis on pricing and hedging the longevity risk, interest rate risk and equity risk for the GMBs embedded in VAs, and highlight the benefits to insurance providers who offer those products.

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  • 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.
    • Handle: RePEc:eee:insuma:v:70:y:2016:i:c:p:286-300
    DOI: 10.1016/j.insmatheco.2016.06.014
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    1. 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.
    2. Gabriella Piscopo & Steven Haberman, 2011. "The Valuation of Guaranteed Lifelong Withdrawal Benefit Options in Variable Annuity Contracts and the Impact of Mortality Risk," North American Actuarial Journal, Taylor & Francis Journals, vol. 15(1), pages 59-76.
    3. T. R. Hurd & Zhuowei Zhou, 2009. "A Fourier transform method for spread option pricing," Papers 0902.3643, arXiv.org.
    4. Andreas Milidonis & Yijia Lin & Samuel Cox, 2011. "Mortality Regimes and Pricing," North American Actuarial Journal, Taylor & Francis Journals, vol. 15(2), pages 266-289.
    5. Elisa Luciano & Elena Vigna, 2005. "Non mean reverting affine processes for stochastic mortality," ICER Working Papers - Applied Mathematics Series 4-2005, ICER - International Centre for Economic Research.
    6. Yang Shen & Kun Fan & Tak Kuen Siu, 2014. "Option Valuation Under a Double Regime‐Switching Model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 34(5), pages 451-478, May.
    7. 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.
    8. 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.
    9. Schrager, David F., 2006. "Affine stochastic mortality," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 81-97, February.
    10. Dahl, Mikkel, 2004. "Stochastic mortality in life insurance: market reserves and mortality-linked insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 35(1), pages 113-136, August.
    11. Darrell Duffie & Rui Kan, 1996. "A Yield‐Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406, October.
    12. Robert J. Elliott & Leunglung Chan & Tak Kuen Siu, 2005. "Option pricing and Esscher transform under regime switching," Annals of Finance, Springer, vol. 1(4), pages 423-432, October.
    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. Andrew J. G. Cairns & David Blake & Kevin Dowd, 2006. "A Two‐Factor Model for Stochastic Mortality with Parameter Uncertainty: Theory and Calibration," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(4), pages 687-718, December.
    15. Fung, Man Chung & Ignatieva, Katja & Sherris, Michael, 2014. "Systematic mortality risk: An analysis of guaranteed lifetime withdrawal benefits in variable annuities," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 103-115.
    16. Bauer, Daniel & Kling, Alexander & Russ, Jochen, 2008. "A Universal Pricing Framework for Guaranteed Minimum Benefits in Variable Annuities 1," ASTIN Bulletin, Cambridge University Press, vol. 38(2), pages 621-651, November.
    17. 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.
    18. 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.
    19. 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.
    20. Milevsky, Moshe A. & David Promislow, S., 2001. "Mortality derivatives and the option to annuitise," Insurance: Mathematics and Economics, Elsevier, vol. 29(3), pages 299-318, December.
    21. 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. Karim Barigou & Lukasz Delong, 2021. "Pricing equity-linked life insurance contracts with multiple risk factors by neural networks," Post-Print hal-02896141, HAL.
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    3. 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.
    4. Charles Guy Njike Leunga & Donatien Hainaut, 2022. "Valuation of Annuity Guarantees Under a Self-Exciting Switching Jump Model," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 963-990, June.
    5. Huang, Yiming & Mamon, Rogemar & Xiong, Heng, 2022. "Valuing guaranteed minimum accumulation benefits by a change of numéraire approach," Insurance: Mathematics and Economics, Elsevier, vol. 103(C), pages 1-26.
    6. Karim Barigou & Daniel Linders & Fan Yang, 2021. "Actuarial-consistency and two-step actuarial valuations: a new paradigm to insurance valuation," Papers 2109.13796, arXiv.org, revised Mar 2022.
    7. Karim Barigou & Daniël Linders & Fan yang, 2022. "Actuarial-consistency and two-step actuarial valuations: a new paradigm to insurance valuation," Working Papers hal-03327710, HAL.
    8. Wanying Fu & Barry R. Smith & Patrick Brewer & Sean Droms, 2023. "Markov-Switching Bayesian Vector Autoregression Model in Mortality Forecasting," Risks, MDPI, vol. 11(9), pages 1-23, August.
    9. Godin, Frédéric & Lai, Van Son & Trottier, Denis-Alexandre, 2019. "Option pricing under regime-switching models: Novel approaches removing path-dependence," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 130-142.
    10. Man Chung Fung & Katja Ignatieva & Michael Sherris, 2019. "Managing Systematic Mortality Risk in Life Annuities: An Application of Longevity Derivatives," Risks, MDPI, vol. 7(1), pages 1-25, January.
    11. 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.
    12. Wenguang Yu & Yaodi Yong & Guofeng Guan & Yujuan Huang & Wen Su & Chaoran Cui, 2019. "Valuing Guaranteed Minimum Death Benefits by Cosine Series Expansion," Mathematics, MDPI, vol. 7(9), pages 1-15, September.
    13. 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.
    14. Siu, Tak Kuen, 2023. "European option pricing with market frictions, regime switches and model uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 233-250.
    15. Karim Barigou & Lukasz Delong, 2021. "Pricing equity-linked life insurance contracts with multiple risk factors by neural networks," Working Papers hal-02896141, HAL.
    16. Nguyen, Hang & Sherris, Michael & Villegas, Andrés M. & Ziveyi, Jonathan, 2024. "Scenario selection with LASSO regression for the valuation of variable annuity portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 116(C), pages 27-43.
    17. Wenlong Hu, 2020. "Risk management of guaranteed minimum maturity benefits under stochastic mortality and regime-switching by Fourier space time-stepping framework," Papers 2006.15483, arXiv.org, revised Dec 2020.
    18. Wanying Fu & Barry R. Smith & Patrick Brewer & Sean Droms, 2022. "A New Mortality Framework to Identify Trends and Structural Changes in Mortality Improvement and Its Application in Forecasting," Risks, MDPI, vol. 10(8), pages 1-38, August.
    19. Karim Barigou & Daniël Linders & Fan Yang, 2022. "Actuarial-consistency and two-step actuarial valuations: a new paradigm to insurance valuation," Post-Print hal-03327710, HAL.
    20. Fontana, Claudio & Rotondi, Francesco, 2023. "Valuation of general GMWB annuities in a low interest rate environment," Insurance: Mathematics and Economics, Elsevier, vol. 112(C), pages 142-167.
    21. Jennifer Alonso Garcia & Michael Sherris & Samuel Thirurajah & Jonathan Ziveyi, 2020. "Taxation and policyholder behavior: the case of guaranteed minimum accumulation benefits," ULB Institutional Repository 2013/307889, ULB -- Universite Libre de Bruxelles.

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    More about this item

    Keywords

    Variable annuity; Guaranteed Minimum Benefits (GMB); Fourier Space Time-stepping (FST) algorithm; Mortality risk; Interest rate risk;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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