High age mortality convergence

Large variations in mortality are often observed at working ages for different subgroups of the population. These differentials have been observed to persist past retirement, but appear to diminish at older ages, this is “high age mortality convergence”. The extent to which, if any, subgroup mortality curves converge past retirement is a difficult question to answer as the low data volumes at very high ages undermine the statistical significance of any results found.

High age mortality convergence has the greatest influence on calculations involving those in the population who are ‘oldest’. Calculations affected include computing quantities such as valuations of annuities, pension scheme liabilities and whole of life assurances. Using mortality rates which differ significantly from population mortality at high ages to value these products might produce what appears like reasonable results on a present value basis at the valuation date however their use could be misleading. For example, a mismatch between the assumed and ‘true’ shape of mortality can lead to:

• Instability in the basis over time
• Misunderstandings in the emergence of profit
• Difficulty in interpreting emerging experience

The following questions should be a useful starting point for considering the high-age implications of your mortality basis on your valuation:

• Does the basis converge towards population mortality rates at high ages?
• If there are separate bases for different subsets of the business, do they converge at high ages?
• What is the financial significance of modelling error with regard to high-age mortality convergence?