Impact of correlation between interest rates and mortality rates on the valuation of various life insurance products

Griselda Deelstra, Pierre Devolder and Benjamin Roelants du Vivier ()
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Pierre Devolder: Université catholique de Louvain, LIDAM/ISBA, Belgium
Benjamin Roelants du Vivier: Université Libre de Bruxelles

No 2024018, LIDAM Reprints ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: In this paper, we question the traditional independence assumption between mortality risk and financial risk and model the correlation between these two risks, estimating its impact on the price of different life insurance products. The interest rate and the mortality intensity are modelled as two correlated Hull and White models in an affine set- up. We introduce two building blocks, namely the zero-coupon survival bond and the mortality density, calculate them in closed form and perform an investigation about their dependence on the correlation between mortality and financial risk, both with theoretical results and numerical analysis. We study the impact of correlation also for more structured insurance products, such as pure endowment, annuity, term insurance, whole life insurance and mixed endowment. We show that in some cases, the inclusion of correlation can lead to a severe underestimation or overestimation of the best estimate. Finally, we illustrate that the results obtained using a traditional affine diffusive set-up can be generalised to affine jump diffusion by computing the price of the zero-coupon survival bond in the presence of jumps.

Keywords: Stochastic mortality; correlation between mortality and financial risks; zero-coupon survival bond; mortality density; affine jump diffusion (search for similar items in EconPapers)
Pages: 31
Date: 2024-05-06
Note: In: Astin Bulletin, 2024
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Persistent link: https://EconPapers.repec.org/RePEc:aiz:louvar:2024018

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