Definition
Hazard rate is the instantaneous rate at which an event of interest occurs at a specified age, conditional on the event not yet having occurred — in mortality applications, the rate of death at a given age among those still alive at that age.
Why it matters
Hazard rate is the structural core that mortality science is built on. Life expectancy, the survival curve, mortality tables, and most actuarial pricing concepts are all derived from age-specific hazard rates; understanding what the hazard rate measures is what makes the relationship between these concepts visible.
How it works
The hazard rate at a given age is calculated as the probability of dying within a short interval at that age, divided by the length of the interval, conditional on being alive at the start of the interval. As the interval shrinks toward zero, the hazard rate becomes an instantaneous rate — a point measure of how rapidly death is occurring among the cohort still alive at that age. The hazard rate rises sharply with adult age, reflecting biological aging. Concrete worked figures for a US female: at age 67, the annual hazard is roughly 1 in 100; by age 85 it has risen to roughly 1 in 15; by age 95 it is roughly 1 in 5. The conditional structure is what distinguishes hazard rates from raw population mortality counts — at each age, the denominator is only those who have survived to that age, which is why hazard rates rise even when the raw number of deaths per calendar year is declining at very advanced ages.
In practice
For an individual, hazard rates are not typically encountered directly, but every annuity quote, life insurance premium, and longevity-risk calculation they are presented with depends on them. The most useful intuition is that the hazard rate is the conditional rate of dying given that one has survived to a given age — it explains why a 95-year-old's annuity payout rate is dramatically higher than a 65-year-old's even at the same insurer load. A professional working from mortality tables is working with hazard rates in a particular tabular form, and the participant should be able to ask whether the rates are drawn from a period table, a cohort table, or a projected table.
In the Longevity Standard Framework
Hazard rate is the structural mechanism underlying age-specific mortality measurement in the Longevity Standard framework's actuarial engine. The engine uses Gompertz-form hazard rates with female focal parameters (m=89, b=10), scaled by Society of Actuaries credibility tables, to produce the survival probabilities that drive the framework's cost-of-income calculations across solo drawdown, the frictionless pool, and the SPIA and DIA product benchmarks. Mortality credits — the structural mechanism by which pooling produces more income per dollar than self-management — are the per-period release of hazard-rate-driven survival decline into the pool's surviving members.
Related terms
- Force of mortality
- Mortality rate
- Survival curve
- Gompertz law
- Life expectancy
- Mortality table
- Mortality credits
- Longevity risk