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Analysis of Deferred Annuity Values Under Different Mortality Assumptions

Abstract

Deferred annuities are life insurance products in which benefit payments commence after a specified period, with the value of the contract depending substantially on the probability that the policyholder survives to the commencement and subsequent payment periods. Mortality assumptions are therefore important actuarial inputs in determining deferred annuity values. Differences in mortality assumptions can produce variations in expected survival probabilities, future benefit payments, and the present value of annuity obligations. This study analyses deferred annuity values under different mortality assumptions. It will examine how variations in assumed mortality rates influence the actuarial value of deferred annuity contracts. The study will focus on the effect of mortality assumptions on survival probabilities, expected payment periods, and the present value of future annuity benefits. The analysis will consider alternative mortality assumptions representing different levels of mortality experience. Actuarial life tables and survival probabilities will be used to estimate the likelihood of policyholders surviving through the deferral period and receiving subsequent annuity payments. The study will also examine how changes in mortality assumptions affect the duration and value of expected annuity payments. A quantitative actuarial research approach will be adopted for the study. Relevant mortality data and actuarial life tables will be analysed using survival probability calculations and annuity valuation techniques. Scenario analysis will be applied to compare deferred annuity values under alternative mortality assumptions, while present value calculations will be used to determine the financial implications of differences in expected survival patterns. The study is expected to show that deferred annuity values will vary under different mortality assumptions. Lower assumed mortality rates are expected to produce higher annuity values because greater survival probabilities may result in longer periods of expected benefit payments. Conversely, higher mortality assumptions are expected to reduce the expected duration of payments and consequently lower the actuarial value of deferred annuity obligations. The study is expected to provide useful information for actuaries, insurers, and pension practitioners involved in annuity valuation and product design. The findings may assist in evaluating the sensitivity of deferred annuity values to mortality assumptions and improving the selection of appropriate mortality bases. The study may also support more accurate estimation of future annuity liabilities and financial requirements. The study concludes that mortality assumptions are an important determinant of deferred annuity values because they directly influence survival probabilities and expected future benefit payments. It is therefore recommended that insurers and actuaries regularly review mortality assumptions and incorporate relevant mortality experience into annuity valuation models. Appropriate sensitivity and scenario analysis should also be applied to assess the effect of alternative mortality assumptions on deferred annuity values.

Keywords: Deferred annuities, annuity valuation, mortality assumptions, mortality rates, survival probabilities, actuarial valuation, life tables, annuity benefits, deferred benefits, present value, longevity risk, mortality experience, actuarial models, insurance liabilities, annuity pricing.