MODELLING MORTALITY RATES FOR LIFE INSURANCE PREMIUM DETERMINATION

CHAPTER ONE

INTRODUCTION

1.1 Background to the Study

The life insurance contract is, at its core, a wager on the timing of death. The insurer promises a benefit payable on the death of the life assured, and in exchange receives a premium calculated so that, across a large pool of similar lives, the discounted value of premiums received equals the discounted value of benefits paid plus a margin for expenses, profit and adverse deviation. The instrument that makes this calculation possible is the mortality table a schedule of age-specific probabilities of death from which survival probabilities, expected present values of annuities and assurances, and ultimately net and office premiums are derived.

For most of the history of the profession, mortality tables were treated as deterministic. Rates were graduated from observed experience, published as a standard table, and applied for years or decades without revision. This practice became untenable once it was recognised that mortality is not static but evolves stochastically over time. Lee and Carter (1992) introduced the first widely adopted stochastic mortality model, expressing the logarithm of the age-specific central death rate as the sum of an age-specific level, an age-specific sensitivity parameter, and a time-varying mortality index which is itself forecast by a time series process. The model's simplicity and forecasting performance led to its adoption across a wide range of national populations. Subsequent extensions the age–period–cohort formulation of Renshaw and Haberman (2006), the two-factor stochastic model of Cairns, Blake and Dowd (2006), and the Poisson log-bilinear estimation of Brouhns, Denuit and Vermunt (2002) addressed limitations of the original specification, while recent work has hybridised the Lee–Carter structure with ARIMA, random forest and neural network methods (Nigri, Levantesi, Marino, Scognamiglio, & Perla, 2019; Wang, Zhang, & Ng, 2020).

The practical importance of this literature is that mis-specified mortality assumptions translate directly into mis-priced contracts. Where assumed mortality is heavier than actual experience, term assurance is over-priced and the insurer loses market share; where assumed mortality is lighter than actual, the insurer under-reserves and risks insolvency. In annuity business the exposure runs in the opposite direction, so that a single table cannot serve both product lines prudently.

Nigeria's position in this landscape is distinctive and problematic. Life expectancy at birth stands at approximately 54.6 years, against a world average of about 73.9 years (World Bank, 2026), and the mortality profile is heavily weighted towards early-life deaths, with Nigeria carrying the highest under-five mortality burden in Africa. Yet the country has no regularly updated national mortality table derived from insured lives experience. Nigerian life offices have historically relied on the English A67/70 table and other foreign standard tables, adjusted by judgment, because civil registration captures only a minority of deaths and because insured-lives experience data have not been systematically pooled. This occurs at precisely the moment when accurate mortality assumptions matter most: annuities accounted for 44.3 per cent of life insurance premiums in 2025, life business generated ₦674.3 billion in the first half of 2025 alone (National Insurance Commission [NAICOM], 2026), and the risk-based capital regime introduced by the Nigerian Insurance Industry Reform Act, 2025 requires insurers to quantify the capital consequences of mortality and longevity risk. This study therefore sets out to model

Nigerian mortality rates using stochastic mortality models and to apply the fitted rates to the determination of life insurance premiums.

1.2 Statement of the Problem

Nigerian life insurers price mortality risk using tables that were not constructed from Nigerian experience. This creates three distinct problems.

First, basis risk. A table graduated from British or South African insured-lives experience embeds the age pattern of mortality of those populations. Nigeria's mortality curve differs materially in shape, not merely in level infant and young-adult mortality are proportionately far higher, and the rate of improvement at older ages differs. Applying a foreign table with a flat percentage adjustment does not correct a difference in shape.

Second, the absence of a mortality improvement assumption. Even where a base table is chosen sensibly, prudent pricing of long-term contracts requires a projection of how mortality will change over the life of the contract. Nigerian practice generally lacks any such projection, which leaves annuity portfolios exposed to longevity risk and term assurance portfolios exposed to unanticipated mortality deterioration.

Third, data scarcity and the estimation problem it creates. Nigeria's civil registration and vital statistics system is incomplete, so the exposure and death counts needed to fit models such as Lee–Carter must be assembled from survey-based estimates, model life tables, and whatever insured-lives data can be obtained. It has not been established in the Nigerian literature whether stochastic mortality models can be fitted reliably to such data, which model specification performs best, or how much premium rates would change if locally fitted rates replaced the foreign tables currently in use. The problem this study addresses is the

absence of empirically fitted Nigerian mortality models and of evidence on the premium consequences of continuing to price with foreign tables.

1.3 Aim and Objectives of the Study

The aim of this study is to model mortality rates in Nigeria and to apply the fitted rates to the determination of life insurance premiums.

The specific objectives are to:

1. examine the pattern and trend of age-specific mortality rates in Nigeria over the study period;

2. fit the Lee–Carter model and selected alternative stochastic mortality models to Nigerian mortality data;

3. compare the fitted models on the basis of goodness of fit and forecast accuracy;

4. forecast age-specific mortality rates for a defined projection horizon using the best-fitting model;

5. construct a mortality table from the fitted and forecast rates.

1.4 Research Questions

1. What is the pattern and trend of age-specific mortality rates in Nigeria over the study period?

2. How well does the Lee–Carter model fit Nigerian mortality data relative to alternative stochastic mortality models?

3. Which model provides the most accurate out-of-sample mortality forecasts for Nigeria?

4. What age-specific mortality rates are projected for Nigeria over the forecast horizon?

5. What premiums for selected life assurance and annuity contracts result from the constructed mortality table?

1.5 Research Hypotheses

The following null hypotheses will be tested at the 5% level of significance:

H₀₁: There is no significant downward trend in age-specific mortality rates in Nigeria over the study period.

H₀₂: The Lee–Carter model does not provide a significantly better fit to Nigerian mortality data than alternative stochastic mortality models.

H₀₃: There is no significant difference in forecast accuracy among the candidate mortality models.

H₀₄: There is no significant difference between premiums computed from the locally constructed mortality table and those computed from the standard tables currently in use.

1.6 Significance of the Study

For life insurance companies, the study offers a mortality basis grounded in Nigerian experience, which bears directly on the adequacy of premium rates, reserves and the pricing of the rapidly growing annuity book. For NAICOM and the Financial Reporting Council of Nigeria, it provides a reference basis against which insurers' submitted valuation assumptions can be reviewed under the risk-based capital framework of NIIRA 2025, and evidence bearing on the case for a national insured-lives mortality investigation. For the Nigerian Actuarial Society, the study contributes to the technical infrastructure standard tables, improvement scales, graduation methods on which a domestic actuarial profession depends. For pension fund administrators and PenCom, projected mortality rates are an input to the pricing of programmed withdrawal and retiree life annuity options. For policyholders, more accurate mortality assumptions mean fairer premiums and more secure benefits. For scholarship, the study extends the stochastic mortality modelling literature overwhelmingly developed on high-quality data from developed countries to a setting characterised by incomplete registration, thereby testing the robustness of these methods under data constraints typical of sub-Saharan Africa.

1.7 Scope of the Study

The study covers Nigerian mortality data over a period of not less than twenty years, drawn from the World Health Organization mortality database, the United Nations World Population Prospects, World Bank World Development Indicators, National Population Commission and Nigeria Demographic and Health Survey estimates, and, where accessible, insured-lives experience data from Nigerian life offices. Mortality is modelled by single year or five-year age group and by sex. The modelling scope is restricted to discrete-time stochastic mortality models Lee–Carter and its Poisson log-bilinear, age–period–cohort and two-factor extensions, together with ARIMA-based and hybrid machine-learning forecasting of the mortality index. The premium application covers whole life assurance, term assurance, endowment assurance and immediate life annuity contracts at selected ages and terms. The study does not extend to morbidity, disability or critical illness rates, nor to the pricing of with-profits or unit-linked contracts.

1.8 Limitations of the Study

(i) Incomplete vital registration Nigeria records only a minority of deaths through civil registration, so the study must rely substantially on modelled and survey-derived mortality estimates, which carry their own estimation error and are themselves partly model-dependent. (ii) Data granularity mortality estimates for Nigeria are frequently published in five-year age bands and at five-year intervals, which limits the resolution at which age and period effects can be identified. (iii) Insured-lives data access life offices treat experience data as commercially confidential, so population mortality may have to serve as a proxy for insured-lives mortality despite the well-documented selection effect that makes insured lives lighter than the general population. (iv) Structural instability mortality shocks during the study period, including the COVID-19 pandemic and periods of armed conflict and epidemic disease, may distort the estimated mortality index and complicate its extrapolation. (v) Extrapolation uncertainty forecast mortality rates carry widening confidence intervals over the projection horizon, and premium calculations inherit that uncertainty.

1.9 Operational Definition of Terms

Mortality rate: The proportion of a defined population that dies within a specified period; the central death rate m(x,t) relates deaths at age x in year t to the corresponding central exposure to risk.

Force of mortality, μ(x): The instantaneous rate of death at exact age x.

Mortality table (life table): A tabulation of age-specific mortality and survival probabilities for a defined population, from which actuarial functions are derived.

Lee–Carter model: A stochastic mortality model expressing log central death rates as a₍ₓ₎ + b₍ₓ₎k₍ₜ₎ + ε₍ₓ,ₜ₎, where k₍ₜ₎ is a time-varying mortality index forecast by a time series process.

Graduation: The process of smoothing observed crude mortality rates to produce a progression consistent with the presumed underlying law of mortality.

Net premium: The premium calculated on mortality and interest assumptions only, without allowance for expenses, profit or contingency margins.

Office premium (gross premium): The premium actually charged, comprising the net premium plus loadings for expenses, profit and adverse deviation.

Longevity risk: The risk that lives assured, particularly annuitants, survive longer than assumed, increasing the insurer's liability.

Mortality improvement: The tendency of age-specific mortality rates to decline over calendar time.

References

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