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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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    2. Markus Hess, 2018. "Cliquet option pricing in a jump-diffusion L\'{e}vy model," Papers 1810.09670, arXiv.org.
    3. 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.
    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. 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.
    6. 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.
    7. 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.

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