Longevity risk in portfolios of pension annuities

• Published in: Insurance, mathematics & economics Vol. 42; no. 2; pp. 505 - 519
• Main Authors: Hári, Norbert, De Waegenaere, Anja, Melenberg, Bertrand, Nijman, Theo E.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.04.2008; Elsevier; Elsevier Sequoia S.A
• Series: Insurance: Mathematics and Economics
• Subjects: Annuities; Funding ratio; Investment theory; Life insurance; Liquidity; Longevity risk; Mathematical economics; Mathematical finance; Mathematical models; Mortality; Mortality projection; Pension fund; Pension funds; Population statistics; Portfolio management; Risk; Risk assessment; Solvency buffer; Studies; Uncertainty; Solvency buffer; Funding ratio; Pension fund; Longevity risk; G23; E47; J11; Mortality projection
• ISSN: 0167-6687; 1873-5959
• DOI: 10.1016/j.insmatheco.2007.01.012

We analyze the importance of longevity risk for the solvency of portfolios of pension annuities. We distinguish two types of mortality risk. Micro-longevity risk quantifies the risk related to uncertainty in the time of death if survival probabilities are known with certainty, while macro-longevity risk is due to uncertain future survival probabilities. We use a generalized two-factor Lee–Carter mortality model to produce forecasts of future mortality rates, and to assess the relative importance of micro- and macro-longevity risk for funding ratio uncertainty. The results show that if financial market risk is fully hedged so that uncertainty in future lifetime is the only source of uncertainty, pension funds are exposed to a substantial amount of risk. Systematic and non-systematic deviations from expected survival imply that, depending on the size of the portfolio, buffers that reduce the probability of underfunding to 2.5% at a 5-year horizon have to be of the order of magnitude of 7% to 8% of the initial value of the liabilities.