Managing Systematic Mortality Risk in Life Annuities: An Application of Longevity Derivatives

This paper assesses the hedge effectiveness of an index-based longevity swap and a longevity cap for a life annuity portfolio. Although longevity swaps are a natural instrument for hedging longevity risk, derivatives with non-linear pay-offs, such as longevity caps, provide more effective downside protection. A tractable stochastic mortality model with age dependent drift and volatility is developed and analytical formulae for prices of longevity derivatives are derived. The model is calibrated using Australian mortality data. The hedging of the life annuity portfolio is comprehensively assessed for a range of assumptions for the longevity risk premium, the term to maturity of the hedging instruments, as well as the size of the underlying annuity portfolio. The results compare the risk management benefits and costs of longevity derivatives with linear and nonlinear payoff structures.

Assessing basis risk in index-based longevity swap transactions

In this paper, we carry out an investigation on modelling basis risk and measuring risk reduction in a longevity hedge constructed by index-based longevity swaps. We derive the fitting procedures of the M7-M5 and common age effect+Cohorts models and define the level of longevity risk reduction. Based on a wide range of hedging scenarios of pension plans, we find that the risk reduction levels are often around 50%–80% for a large plan, while the risk reduction estimates are usually smaller than 50% for a small plan. Moreover, index-based hedging looks more effective under a more precise hedging scheme. We also perform a detailed sensitivity analysis on the hedging results. The most important modelling features are the behaviour of simulated future variability, portfolio size, speed of reaching coherence, data size and characteristics, simulation method, and mortality structural changes.

Assessing basis risk for longevity transactions – phase 2 presented by Dr Jackie Li and Dr Chong It Tan, IFoA Longevity Basis Risk Working Group ‐ Abstract of the London Discussion

This abstract relates to the following paper: LiJ., LiJ. S. H., TanC. I. and TickleL. (2018) Assessing basis risk in index-based longevity swap transactions. Annals of Actuarial Science. Cambridge University Press, doi: 10.1017/S1748499518000179.