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Cliquet-style return guarantees in a regime switching Lévy model

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  • Hieber, Peter

Abstract

This article considers the valuation of equity-linked life insurance contracts that offer an annually guaranteed minimum return. The policy premiums are invested in a reference portfolio that is modeled by means of a regime switching Lévy process where the model parameters depend on a continuous-time, finite state Markov chain. Thereby, we can take into account persistent changes in the underlying (macro)economic conditions of financial markets and depart from the unsatisfactory assumption of stationary and independent increments in Lévy models. While Lévy models turn out to be satisfactory for the valuation of short-term financial contracts, the inclusion of macroeconomic changes is a relevant risk driver for (long-term) insurance contracts. This article demonstrates that a second advantage of regime switching Lévy models is their mathematical tractability: In contrast to a large part of the related literature, the results in this article do not rely on simulation but are easy-to-implement and closed-form expressions based on (fast) Fourier techniques. A numerical example demonstrates the impact of regime switching on the fair value of cliquet-style return guarantees.

Suggested Citation

  • Hieber, Peter, 2017. "Cliquet-style return guarantees in a regime switching Lévy model," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 138-147.
    • Handle: RePEc:eee:insuma:v:72:y:2017:i:c:p:138-147
    DOI: 10.1016/j.insmatheco.2016.11.009
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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Yayun Wang, 2023. "Pricing a Specific Equity Index Annuity in a Regime-Switching Lévy Model with Jump," Computational Economics, Springer;Society for Computational Economics, vol. 61(3), pages 1115-1135, March.
    6. Olivier Le Courtois & François Quittard-Pinon & Xiaoshan Su, 2020. "Pricing and hedging defaultable participating contracts with regime switching and jump risk," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 303-339, June.
    7. Ludovic Gouden`ege & Andrea Molent & Antonino Zanette, 2025. "Robust Pricing of Equity-Indexed Annuities under Uncertain Volatility and Stochastic Interest Rate," Papers 2502.10300, arXiv.org, revised Feb 2025.
    8. Markus Hess, 2018. "Cliquet option pricing in a jump-diffusion L\'{e}vy model," Papers 1810.09670, arXiv.org.
    9. Ludovic Gouden`ege & Andrea Molent & Xiao Wei & Antonino Zanette, 2024. "Enhancing Valuation of Variable Annuities in L\'evy Models with Stochastic Interest Rate," Papers 2404.07658, arXiv.org.
    10. Yaodi Yong & Hailiang Yang, 2021. "Valuation of Cliquet-Style Guarantees with Death Benefits in Jump Diffusion Models," Mathematics, MDPI, vol. 9(16), pages 1-21, August.
    11. 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.

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