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Pricing of Ratchet equity-indexed annuities under stochastic interest rates

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  • Kijima, Masaaki
  • Wong, Tony

Abstract

We consider the valuation of simple and compound Ratchet equity-indexed annuities (EIAs) in the presence of stochastic interest rates. We assume that the equity index follows a geometric Brownian motion and the short rate follows the extended Vasicek model. Under a given forward measure, we obtain an explicit multivariate normal characterization for multiple log-returns on the equity index. Using such a characterization, closed-form price formulas are derived for both simple and compound Ratchet EIAs. An efficient Monte Carlo simulation scheme is also established to overcome the computational difficulties resulting from the evaluation of high-dimensional multivariate normal cumulative distribution functions (CDFs) embedded in the price formulas as well as the consideration of additional complex contract features. Finally, numerical results are provided to illustrate the computational efficiency of our simulation scheme and the effects of various model and contract parameters on pricing.

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  • Kijima, Masaaki & Wong, Tony, 2007. "Pricing of Ratchet equity-indexed annuities under stochastic interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 41(3), pages 317-338, November.
    • Handle: RePEc:eee:insuma:v:41:y:2007:i:3:p:317-338
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    7. Kirkby, J. Lars, 2023. "Hybrid equity swap, cap, and floor pricing under stochastic interest by Markov chain approximation," European Journal of Operational Research, Elsevier, vol. 305(2), pages 961-978.
    8. 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.
    9. Jingjiang Peng & Kwai Sun Leung & Yue Kuen Kwok, 2012. "Pricing guaranteed minimum withdrawal benefits under stochastic interest rates," Quantitative Finance, Taylor & Francis Journals, vol. 12(6), pages 933-941, October.
    10. Gan, Guojun, 2013. "Application of data clustering and machine learning in variable annuity valuation," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 795-801.
    11. Jr-Wei Huang & Sharon S. Yang & Chuang-Chang Chang, 2021. "Modeling Housing Price Dynamics and their Impact on the Cost of no-Negative-Equity-Guarantees for Equity Releasing Products," The Journal of Real Estate Finance and Economics, Springer, vol. 63(2), pages 249-279, August.
    12. 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.
    13. Yuanchuang Shan & Huisheng Shu & Haoran Yi, 2023. "Pricing Equity-Indexed Annuities under a Stochastic Dividend Model," Mathematics, MDPI, vol. 11(3), pages 1-12, January.
    14. 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.
    15. 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.
    16. Chiu, Yu-Fen & Hsieh, Ming-Hua & Tsai, Chenghsien, 2019. "Valuation and analysis on complex equity indexed annuities," Pacific-Basin Finance Journal, Elsevier, vol. 57(C).
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