Title: Pricing longevity bonds using a generalised Vasicek term structure model with correlated mortality and interest rates

Authors: Georgina Onuma Kalu; Dennis Ikpe; Ben Ifeanyichukwu Oruh

Addresses: Department of Mathematical Sciences, University of South Africa, South Africa ' Department of Probability and Statistics, Michigan State University, Lansing, USA; Department of Mathematical Sciences, University of South Africa, Pretoria, South Africa ' Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Nigeria

Abstract: Longevity risk, defined as the possibility that individuals live longer than anticipated, presents substantial challenges for pension funds and annuity providers. This risk can increase financial liabilities, as the actual pay out obligations may exceed initial projections. To address this issue, this study proposes a novel pricing approach for zero-coupon longevity bonds. The methodology employs a generalised Vasicek term structure model, effectively capturing the intricate relationship between mortality and interest rates. This model extends the classical one-factor affine Vasicek framework by jointly modelling the dynamics of the instantaneous forward mortality rate and the instantaneous interest rate within a state space context. The application of this model allows for more accurate pricing of longevity bonds, facilitating better risk management for pension funds and annuity providers. By accounting for the correlation between mortality and interest rates, the findings underscore the importance of sophisticated modelling techniques in managing longevity risk. The results indicate that traditional methods may inadequately capture the complexities involved in pricing longevity-linked securities. This research contributes to the ongoing discourse on effective strategies for mitigating longevity risk in financial markets, thereby supporting pension funds and annuity providers in their efforts to ensure financial stability.

Keywords: zero-coupon longevity bond; longevity risk; pension fund; annuity providers; financial liabilities.

DOI: 10.1504/IJBD.2025.148703

International Journal of Bonds and Derivatives, 2025 Vol.4 No.4, pp.359 - 381

Received: 05 Aug 2024
Accepted: 06 Feb 2025
Published online: 19 Sep 2025 *

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