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We use life annuity prices to extract information about human longevity usinga framework that links the term structure of mortality and interest rates. Weinvert the model and perform nonlinear least squares to obtain impliedlongevity forecasts. Methodologically, we assume a Cox-Ingersoll-Ross (CIR)model for the underlying yield curve, and for mortality, a Gompertz-Makeham(GM) law that varies with the year of annuity purchase. Our main result is thatover the last decade markets implied an improvement in longevity of of 6-7weeks per year for males and 1-3 weeks for females. In the year 2004 marketprices implied a $40.1\%$ probability of survival to the age 90 for a 75-yearold male ($51.2\%$ for a female) annuitant. By the year 2013 the impliedsurvival probability had increased to $46.1\%$ (and $53.1\%$). Thecorresponding implied life expectancy has increased (at the age of 75) from13.09 years for males (15.08 years for females) to 14.28 years (and 15.61years.) Although these values are implied directly from markets, they areconsistent with demographic projections. Similar to implied volatility inoption pricing, we believe that our implied survival probabilities (ISP) andimplied life expectancy (ILE) are relevant for the financial management ofassets post-retirement and very important for the optimal timing and allocationto annuities; procrastinators are swimming against an uncertain but ratherstrong longevity trend.

The implied longevity curve: How long does the market think you are going to live?