Mortality Analysis and Life Tables: How Insurers Price the Risk of Death

In short: A life table translates raw mortality data into a set of age-specific probabilities that actuaries use to price life insurance, calculate policy reserves, and model survival outcomes. The key input is qx — the probability of dying between age x and x+1. Understanding the structure of a life table and how qx rates change with age is the foundation of every actuarial calculation in life insurance.

When an insurer agrees to pay a death benefit of £500,000 if you die within the next 20 years, it is making a promise whose cost depends on one central question: how likely are you to die within that period? The answer is not a guess — it is derived from a life table: a statistical summary of mortality experience across thousands or millions of lives, organised by age, gender, and sometimes smoker status or socioeconomic group.

Life tables are the bedrock of every pricing, reserving, and embedded value calculation in life insurance and annuities. This post covers the structure, construction, and practical application of life tables from the perspective of a financial analyst working alongside actuarial teams.

The Structure of a Life Table

A standard life table contains five core columns:

The relationship between columns is recursive:

lx+1 = lx × px = lx × (1 − qx)
dx   = lx × qx

Starting from l0 = 100,000 lives at birth, the table tracks how many survive to each age and how many die in each year. By age 30, a modern UK male cohort would show roughly 98,500 survivors; by age 65, around 87,000; by age 80, around 58,000.

Reading qx Rates: What the Numbers Say

The qx rate is the single most important column in the life table. For UK males on an assured lives (life insurance) basis:

Three observations every analyst should internalise:

qx rises exponentially with age. The probability of dying between 65 and 66 is approximately 31 times the probability of dying between 25 and 26. This is the Gompertz–Makeham law — the dominant feature of human mortality.

Smoker mortality is substantially higher. At age 45, a male smoker’s qx is typically 1.8–2.5× the non-smoker rate on standard UK tables. Insurers that underwrite without smoker distinction are exposed to significant adverse selection.

Gender differences are material but narrowing. Historically female qx rates were 40–60% lower than male at the same age. The gender gap has narrowed over recent decades as lifestyle factors have converged, and EU gender directive changes to insurance pricing have also shifted how tables are applied commercially.

From qx to Survival Probabilities

For pricing a term life product, you need the probability that a life aged x survives to age x+n — the n-year survival probability, written nPx:

nPx = px × px+1 × px+2 × ... × px+n−1
    = (lx+n / lx)

For a 35-year-old male taking out a 20-year term policy, the probability of surviving to age 55 (i.e. not claiming on a death benefit) is:

20P35 = l55 / l35

Using indicative UK male assured lives data, this would be approximately 0.974 — meaning roughly 97.4% of such policyholders survive to the end of the term and the insurer never pays a death benefit. The expected cost of the death benefit is then weighted by the year-by-year mortality probability, discounted at the risk-free rate, to arrive at a net premium.

UK Standard Tables: CMI and the A/B Series

The Continuous Mortality Investigation (CMI), operated by the Institute and Faculty of Actuaries, produces the authoritative mortality tables for UK insurers:

The CMI improvement model is critical for products with long durations — particularly annuities and with-profits policies. It projects future reductions in qx rates based on observed trends in UK population mortality. A 65-year-old male in 2025 is expected to live considerably longer than a 65-year-old male in 1990, and that improvement is projected to continue. Ignoring this produces a materially understated reserve for annuity liabilities.

Building a Basic Life Table Model in Excel

A life table in Excel requires only three columns of input and derives the rest:

Column A: Age (x)              → 0 to 120
Column B: qx                   → from CMI table (paste in)
Column C: px = 1 − qx
Column D: lx = D_prev × C_prev (start: l0 = 100,000)
Column E: dx = D × B

For pricing a 10-year term assurance policy at sum assured S for a life aged 40:

1. Extract the qx rates for ages 40–49 from the standard table.
2. For each year, compute the probability of dying in that year from the policy start: qx × (product of all previous px).
3. Discount each expected death benefit payment back to policy start using the risk-free rate.
4. Sum: this is the net single premium — the present value of expected claims.
5. Convert to a level annual premium using the survival-weighted annuity factor.

This Excel calculation mirrors exactly what the insurer’s pricing actuary does — the difference is scale (modelling millions of policies) and the use of proprietary rather than published tables.

Mortality Experience vs Table Assumptions

Standard tables are external benchmarks. Every insurer’s actual policyholders may experience different mortality — better (because they underwrite carefully and insure healthier lives) or worse (because their distribution attracts higher-risk customers). The gap between actual and expected mortality is the subject of experience analysis, covered in post 24. The key measure is the Standardised Mortality Ratio (SMR):

SMR = Actual Deaths / Expected Deaths (from standard table)

An SMR of 80% means actual deaths are 80% of what the standard table predicted — mortality experience is better than the table, which is favourable for a life insurer but unfavourable for an annuity provider. Monitoring SMR over time is how actuaries decide whether the pricing basis needs to be updated.

Key Takeaways

• A life table maps qx (the probability of dying in a given year) by age, forming the statistical basis for all life insurance and annuity calculations.
• qx rises exponentially with age; smoker rates are 1.8–2.5× non-smoker rates; gender differences are material but narrowing.
• The n-year survival probability nPx = lx+n / lx, derived directly from the life table, is the key input to term assurance pricing.
• UK insurers use CMI tables — the A00 series for assured lives, PNXA/B for annuitants — with annual CMI Improvement Model projections for future mortality improvements.
• The Standardised Mortality Ratio (actual deaths / expected deaths) measures how an insurer’s experience compares to the standard table, driving pricing and reserve reviews.

Practice

Download the CMI AM92 male mortality table (available from the Institute and Faculty of Actuaries website). Build a life table in Excel from age 30 to 80. Calculate: (1) the probability that a 40-year-old male survives to age 65; (2) the expected number of deaths between ages 50 and 55 from a starting cohort of 10,000 lives aged 40; (3) the net single premium for a £100,000 death benefit on a 20-year term policy for a 40-year-old male, using a 4% discount rate. Then apply a 20% mortality improvement (multiply all qx by 0.80) and recalculate (3) — explain the direction and magnitude of the change.