How Long Does the Market Think You Will Live? Implying Longevity from Annuity Prices
35 Pages Posted: 15 Jan 2014
Date Written: January 14, 2014
We use life annuity prices to extract information about human longevity by formulating a model that links the term structure of mortality and interest rates. We then invert the model and perform nonlinear least squares to obtain implied longevity forecasts. Methodologically, we assume a Cox-Ingersoll-Ross (CIR) model for the underlying yield curve and a cohort-varying Gompertz-Makeham (GM) law for mortality. Our main result is that over the last decade markets have been implying an improvement in longevity of an average of 6 weeks per year for males and 3 weeks for females. In the year 2004 market prices implied a 40.1% probability of survival to the age 90 for a 75-year old male (51.2% for a female) annuitant. By the year 2013 the implied survival probability had increased to 46.1% (and 53.1%). The corresponding implied life expectancy has increased (at the age of 75) from 13.09 years for males (15.08 years for females) to 14.28 years (and 15.61 years). Although these values are implied directly from markets, they are consistent with demographic projections. Similar to implied volatility in option pricing, we believe that our implied survival probabilities (ISP) and implied life expectancy (ILE) are relevant for the financial management of assets post-retirement and very important for the optimal timing and allocation to annuities; procrastinators are swimming against an uncertain but rather strong longevity trend.
Keywords: wealth management; retirement planning, insurance, annuities, pensions, longevity, aging and demographics
Suggested Citation: Suggested Citation