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Valuation of GLWB-LTC Annuities with L\'evy Equity Dynamics, Stochastic Interest Rates and Health-State Transitions

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  • Andrea Molent

Abstract

This paper develops a valuation framework for guaranteed lifetime withdrawal benefit (GLWB) contracts with long-term care (LTC) features when the reference fund follows exponential Levy dynamics and the short rate follows the Hull-White model. The contract combines financial guarantees, longevity protection, health-contingent LTC payments, and surrender optionality, requiring the joint treatment of jump risk, stochastic discounting, and disability risk. The numerical method couples a recombining Hull-White trinomial tree with an implicit-explicit (IMEX) finite difference scheme. The framework incorporates a seven-state health model, annual fees, LTC payments, guaranteed withdrawals, and bang-bang policyholder actions, and is benchmarked against Monte Carlo simulation. Numerical results show that the hybrid tree-IMEX method delivers stable long-maturity prices consistent with simulation benchmarks. They also show that Levy equity dynamics and stochastic interest rates have a material impact on fair fees and surrender incentives, and affect the decomposition of contract value. The findings highlight the importance of modelling financial tail risk and interest-rate risk jointly when pricing long-term insurance guarantees with LTC-contingent benefits.

Suggested Citation

  • Andrea Molent, 2026. "Valuation of GLWB-LTC Annuities with L\'evy Equity Dynamics, Stochastic Interest Rates and Health-State Transitions," Papers 2605.30567, arXiv.org, revised Jun 2026.
    • Handle: RePEc:arx:papers:2605.30567
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    References listed on IDEAS

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    1. Shaoying Chen & Zhenyu Cui & Zhimin Zhang & Wei Zhong, 2026. "Valuation of GLWB annuities with optional conversion to combo products providing LTC benefits," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2026(3), pages 263-294, March.
    2. Hsieh, Ming-hua & Wang, Jennifer L. & Chiu, Yu-Fen & Chen, Yen-Chih, 2018. "Valuation of variable long-term care Annuities with Guaranteed Lifetime Withdrawal Benefits: A variance reduction approach," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 246-254.
    3. Maya Briani & Lucia Caramellino & Giulia Terenzi & Antonino Zanette, 2019. "Numerical Stability Of A Hybrid Method For Pricing Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(07), pages 1-46, November.
    4. Molent, Andrea, 2020. "Taxation Of A Gmwb Variable Annuity In A Stochastic Interest Rate Model," ASTIN Bulletin, Cambridge University Press, vol. 50(3), pages 1001-1035, September.
    5. Bacinello, Anna Rita & Maggistro, Rosario & Zoccolan, Ivan, 2024. "Risk-neutral valuation of GLWB riders in variable annuities," Insurance: Mathematics and Economics, Elsevier, vol. 114(C), pages 1-14.
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