The implied longevity curve: How long does the market think you are\n going to live?
Bibliographic record
Abstract
We use life annuity prices to extract information about human longevity using\na framework that links the term structure of mortality and interest rates. We\ninvert the model and perform nonlinear least squares to obtain implied\nlongevity forecasts. Methodologically, we assume a Cox-Ingersoll-Ross (CIR)\nmodel for the underlying yield curve, and for mortality, a Gompertz-Makeham\n(GM) law that varies with the year of annuity purchase. Our main result is that\nover the last decade markets implied an improvement in longevity of of 6-7\nweeks per year for males and 1-3 weeks for females. In the year 2004 market\nprices implied a $40.1\\%$ probability of survival to the age 90 for a 75-year\nold male ($51.2\\%$ for a female) annuitant. By the year 2013 the implied\nsurvival probability had increased to $46.1\\%$ (and $53.1\\%$). The\ncorresponding implied life expectancy has increased (at the age of 75) from\n13.09 years for males (15.08 years for females) to 14.28 years (and 15.61\nyears.) Although these values are implied directly from markets, they are\nconsistent with demographic projections. Similar to implied volatility in\noption pricing, we believe that our implied survival probabilities (ISP) and\nimplied life expectancy (ILE) are relevant for the financial management of\nassets post-retirement and very important for the optimal timing and allocation\nto annuities; procrastinators are swimming against an uncertain but rather\nstrong longevity trend.\n
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.035 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.010 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".