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An efficient algorithm for the valuation of a guaranteed annuity option with correlated financial and mortality risks

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  • Zhao, Yixing
  • Mamon, Rogemar

Abstract

We introduce a pricing framework for a guaranteed annuity option (GAO) where both the interest and mortality risks are correlated. We assume that the short rate and the force of mortality follow the Cox–Ingersoll–Ross (CIR) and Lee–Carter models, respectively. Employing the change of measure technique, we decompose the pure endowment into the product of the bond price and survival probability, thereby facilitating the evaluation of the annuity expression. With the aid of the dynamics of interest and mortality processes under the forward measure, we construct an algorithm based on comonotonicity theory to estimate the quantiles of survival probability and annuity rate. The comonotonic upper and lower bounds in the convex order are used to approximate the annuity and GAO prices and henceforth avoiding the simulation-within-simulation problem. Numerical illustrations show that our algorithm gives an efficient and practical method to estimate GAO values.

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  • Zhao, Yixing & Mamon, Rogemar, 2018. "An efficient algorithm for the valuation of a guaranteed annuity option with correlated financial and mortality risks," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 1-12.
    • Handle: RePEc:eee:insuma:v:78:y:2018:i:c:p:1-12
    DOI: 10.1016/j.insmatheco.2017.09.001
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    Cited by:

    1. Zhao, Yixing & Mamon, Rogemar & Gao, Huan, 2018. "A two-decrement model for the valuation and risk measurement of a guaranteed annuity option," Econometrics and Statistics, Elsevier, vol. 8(C), pages 231-249.
    2. Rabitti, Giovanni & Borgonovo, Emanuele, 2020. "Is mortality or interest rate the most important risk in annuity models? A comparison of sensitivity analysis methods," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 48-58.
    3. Da Fonseca, José, 2024. "Pricing guaranteed annuity options in a linear-rational Wishart mortality model," Insurance: Mathematics and Economics, Elsevier, vol. 115(C), pages 122-131.

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