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Longevity bond pricing under stochastic interest rate and mortality with regime-switching

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  • Shen, Yang
  • Siu, Tak Kuen

Abstract

We develop a flexible model to value longevity bonds which incorporates several important sources of risk, namely, interest rate risk, mortality risk and the risk due to structural changes in economic and environmental conditions. In particular, Markov, regime-switching, jump-diffusion models are used to describe stochastic movements of short-term interest rate and force of mortality. These models capture jumps in short rate and mortality rate and the impacts of economic and environmental fundamentals on their movements over time. Using the concept of stochastic flows, we derive an exponential affine form of the longevity bond price in the proposed joint stochastic interest rate and mortality models. In particular, a representation for the exponential affine form of the longevity bond price is obtained in terms of fundamental matrix solutions of linear, matrix-valued, ordinary differential equations.

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  • Shen, Yang & Siu, Tak Kuen, 2013. "Longevity bond pricing under stochastic interest rate and mortality with regime-switching," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 114-123.
    • Handle: RePEc:eee:insuma:v:52:y:2013:i:1:p:114-123
    DOI: 10.1016/j.insmatheco.2012.11.006
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    5. Kogure Atsuyuki & Fushimi Takahiro, 2018. "A Bayesian Pricing of Longevity Derivatives with Interest Rate Risks," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 12(1), pages 1-30, January.
    6. Blake, David & Cairns, Andrew J.G., 2021. "Longevity risk and capital markets: The 2019-20 update," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 395-439.
    7. Ben-zhang Yang & Jia Yue & Nan-jing Huang, 2017. "Variance swaps under L\'{e}vy process with stochastic volatility and stochastic interest rate in incomplete markets," Papers 1712.10105, arXiv.org, revised Mar 2018.
    8. Ben-Zhang Yang & Jia Yue & Nan-Jing Huang, 2019. "Equilibrium Price Of Variance Swaps Under Stochastic Volatility With Lévy Jumps And Stochastic Interest Rate," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(04), pages 1-33, June.
    9. Wanying Fu & Barry R. Smith & Patrick Brewer & Sean Droms, 2023. "Markov-Switching Bayesian Vector Autoregression Model in Mortality Forecasting," Risks, MDPI, vol. 11(9), pages 1-23, August.
    10. Yang, Lin & Pantelous, Athanasios A. & Assa, Hirbod, 2016. "Robust Stability, Stabilisation And H-Infinity Control For Premium-Reserve Models In A Markovian Regime Switching Discrete-Time Framework," ASTIN Bulletin, Cambridge University Press, vol. 46(3), pages 747-778, September.

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