Joint-Survival Annuity Derivative Valuation in the Linear-Rational Wishart Mortality Model
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Da Fonseca, Jose
Wong, Patrick
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Cambridge University Press
Abstract
This paper develops a linear-rational mortality model for couples based on a Wishart state process. The matrix-valued state variable permits a flexible dependence structure between the two mortality intensities while preserving positivity. Within this framework, we derive closed-form expressions for the joint-survival bond and tractable valuation formulas for the joint-survival annuity and the guaranteed joint-survival annuity option. We also characterize the mortality-intensity distribution and retain fast approximation methods for the guaranteed annuity option. To complement the theory, we implement the model on the Canadian dependent-lives portfolio. We benchmark the Wishart model against independence and a Frank copula, and we report the implications for joint-life pricing as well as guaranteed annuity option valuation. The estimation identifies a positive dependence structure consistent with the literature. Moreover, unlike static copula alternatives, the estimated Wishart model feeds directly into the closed-form guaranteed annuity option pricing and approximation formulas developed in the paper, thereby illustrating how the linear-rational Wishart framework can be taken from analytical derivations to a practical dependent-lives implementation.
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4901 Applied Mathematics, 3502 Banking, Finance and Investment, 49 Mathematical Sciences, 0102 Applied Mathematics, 1502 Banking, Finance and Investment, Statistics & Probability, 4905 Statistics, Dependent lives, joint-survival annuity, mortality risk, linear-rational Wishart model, guaranteed annuity option
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ASTIN Bulletin, ISSN: 0515-0361 (Print); 1783-1350 (Online), Cambridge University Press, 1-23. doi: 10.1017/asb.2026.10113
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© The Author(s), 2026. Published by Cambridge University Press on behalf of The International Actuarial Association
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Except where otherwise noted, this item's license is described as Creative Commons Attribution License