Bayesian Integrated Nested Laplace Approximation (INLA) Longevity Bonds Market Model

Pricing coupon longevity bonds (CLBs) is challenging in illiquid markets due to the incompleteness of insurance markets and the unavailability of longevity payout data. In addition, pension funds may experience significant surges in annual mortality-improvement reserves (MIRs), consistent with systematic longevity drift and cohort-survival effects. We propose a Bayesian pricing model based on the Integrated Nested Laplace Approximation (INLA) for CLBs in pension-fund applications. The term structure of interest rates is modeled using a two-factor Cox–Ingersoll–Ross (CIR) specification, while mortality dynamics are captured using a CIR affine jump–diffusion model to capture abrupt longevity shocks. Posterior inference is performed via INLA and benchmarked against Markov chain Monte Carlo (MCMC). Using South African government bond yield data, pension-fund MIR series, and population survival-rate reports, we show that INLA provides a computationally efficient approximation to the MCMC posterior with substantially reduced computation time. Longevity Greeks derived from the model support hedge construction and evaluation of strategies aimed at mitigating rising longevity-linked cash flows. Empirically, model-implied longevity payouts are positively skewed with high dispersion and exhibit frequent jump episodes over a broad range, underscoring the importance of jump risk in CLB valuation and hedging.