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Pricing Variable Annuity Contract with GMAB Guarantee Under a Regime Switching Local Volatility Model

Author

Listed:
  • Sarfraz Mohammad

    (IIT Delhi)

  • Viswanathan Arunachalam

    (Universidad Nacional de Colombia)

  • Dharmaraja Selvamuthu

    (IIT Delhi)

Abstract

This article investigates the pricing of variable annuity guarantees, with particularly emphasising on the Guaranteed Minimum Accumulation Benefit (GMAB) with several embedded options, like roll-up and ratchet. A continuous time model that integrates regime switching dynamics into the local volatility is proposed for the contract’s pricing. As local volatility pioneered by Deelstra and Rayée (2013), on their proposed model by explicitly introducing the regime switching components into the local volatility. Model calibration and valuation are performed through the application of Monte Carlo simulations and Gaussian Process Regression methodologies. For the illustration of the capability of this model and some possible improvements in the model, a numerical and sensitivity analysis is conducted. Uses an empirical test on historical S&P500 Index data to illustrate its practical implications. The results showed that time to maturity, interest rates, and volatilities significantly impact the pricing, and it also illustrates the proposed approach’s accuracy and computational efficiency.

Suggested Citation

  • Sarfraz Mohammad & Viswanathan Arunachalam & Dharmaraja Selvamuthu, 2025. "Pricing Variable Annuity Contract with GMAB Guarantee Under a Regime Switching Local Volatility Model," Computational Economics, Springer;Society for Computational Economics, vol. 66(2), pages 1603-1624, August.
    • Handle: RePEc:kap:compec:v:66:y:2025:i:2:d:10.1007_s10614-024-10764-5
    DOI: 10.1007/s10614-024-10764-5
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    1. 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.
    2. Kang, Boda & Shen, Yang & Zhu, Dan & Ziveyi, Jonathan, 2022. "Valuation of guaranteed minimum maturity benefits under generalised regime-switching models using the Fourier Cosine method," Insurance: Mathematics and Economics, Elsevier, vol. 105(C), pages 96-127.
    3. Griselda Deelstra & Gr�gory Ray�e, 2013. "Local Volatility Pricing Models for Long-Dated FX Derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 20(4), pages 380-402, September.
    4. 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.
    5. 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.
    6. Jan De Spiegeleer & Dilip B. Madan & Sofie Reyners & Wim Schoutens, 2018. "Machine learning for quantitative finance: fast derivative pricing, hedging and fitting," Quantitative Finance, Taylor & Francis Journals, vol. 18(10), pages 1635-1643, October.
    7. 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.
    8. John Buffington & Robert J. Elliott, 2002. "American Options With Regime Switching," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(05), pages 497-514.
    9. 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.
    10. Anthonie W. van der Stoep & Lech A. Grzelak & Cornelis W. Oosterlee, 2017. "A novel Monte Carlo approach to hybrid local volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 17(9), pages 1347-1366, September.
    11. Guojun Gan & X. Sheldon Lin, 2017. "Efficient Greek Calculation of Variable Annuity Portfolios for Dynamic Hedging: A Two-Level Metamodeling Approach," North American Actuarial Journal, Taylor & Francis Journals, vol. 21(2), pages 161-177, April.
    12. Hamilton, James D., 1990. "Analysis of time series subject to changes in regime," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 39-70.
    13. M. Costabile, 2017. "A lattice-based model to evaluate variable annuities with guaranteed minimum withdrawal benefits under a regime-switching model," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2017(3), pages 231-244, March.
    14. 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.
    15. Mary Hardy, 2001. "A Regime-Switching Model of Long-Term Stock Returns," North American Actuarial Journal, Taylor & Francis Journals, vol. 5(2), pages 41-53.
    16. Siu, Tak Kuen, 2005. "Fair valuation of participating policies with surrender options and regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 533-552, December.
    17. Benjamin Jourdain & Alexandre Zhou, 2020. "Existence of a calibrated regime switching local volatility model," Mathematical Finance, Wiley Blackwell, vol. 30(2), pages 501-546, April.
    18. He, Xin-Jiang & Zhu, Song-Ping, 2017. "How should a local regime-switching model be calibrated?," Journal of Economic Dynamics and Control, Elsevier, vol. 78(C), pages 149-163.
    19. Runhuan Feng & Guojun Gan & Ning Zhang, 2022. "Variable annuity pricing, valuation, and risk management: a survey," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2022(10), pages 867-900, November.
    20. Robert J. Elliott & Leunglung Chan & Tak Kuen Siu, 2015. "A Dupire Equation For A Regime-Switching Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(04), pages 1-13.
    21. 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.
    22. Nabil Maghrebi & Mark J. Holmes & Kosuke Oya, 2014. "Financial instability and the short-term dynamics of volatility expectations," Applied Financial Economics, Taylor & Francis Journals, vol. 24(6), pages 377-395, March.
    23. 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.
    24. Robert J. Elliott & Katsumasa Nishide & Carlton‐James U. Osakwe, 2016. "Heston‐Type Stochastic Volatility with a Markov Switching Regime," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 36(9), pages 902-919, September.
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