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Effect of Last-Survivor Mortality Assumptions on Annuity Valuation

Abstract

Last-survivor annuities are designed to provide periodic payments that continue for the lifetime of the last surviving member of a group of insured lives. The valuation of such annuities depends heavily on mortality assumptions because the duration of benefit payments is determined by the survival of the lives covered. Accurate mortality assumptions are therefore essential for estimating the expected duration and actuarial value of last-survivor annuity benefits. This study will examine the effect of last-survivor mortality assumptions on annuity valuation. It will assess the extent to which variations in mortality assumptions influence the actuarial value of last-survivor annuity benefits. The study will also examine how differences in expected survival patterns affect the present value of future annuity payments and the resulting financial obligations of annuity providers. The study will focus on mortality rates, survival probabilities, ages of the insured lives, annuity payment amounts, payment periods, interest rate assumptions, and actuarial present values. Last-survivor actuarial functions will be applied to estimate the probability that at least one of the covered lives remains alive at different future periods. Alternative mortality assumptions will then be used to examine their effects on the valuation of the annuity benefits. A quantitative research approach will be adopted for the study. Relevant mortality data and life table functions will be analysed using survival probability calculations, last-survivor annuity factors, actuarial present value techniques, and scenario analysis. Different mortality assumptions will be applied to comparable annuity contracts, and the resulting valuation estimates will be calculated and compared. The analysis will provide evidence on the sensitivity of last-survivor annuity values to changes in mortality assumptions. The study is expected to reveal that variations in last-survivor mortality assumptions may produce significant differences in annuity valuation estimates. Assumptions indicating longer survival may result in higher actuarial values because annuity payments are expected to continue for longer periods. Conversely, assumptions indicating shorter survival may reduce the expected duration and present value of future payments. The magnitude of the effect is expected to vary according to the ages and mortality characteristics of the lives covered. The study will be useful to actuaries, life insurance companies, pension providers, annuity managers, regulators, and researchers. It may assist in improving the valuation of last-survivor annuities and the assessment of long-term payment obligations. The findings may also support appropriate selection and monitoring of mortality assumptions when pricing, reserving, and valuing multiple-life annuity products. The study concludes that last-survivor mortality assumptions are an important determinant of annuity valuation because they influence the expected duration of benefit payments and their actuarial present value. It is therefore recommended that annuity providers use appropriate and regularly reviewed mortality assumptions when valuing last-survivor annuity contracts to improve the accuracy and reliability of actuarial estimates.

Keywords: Last-survivor mortality assumptions, annuity valuation, last-survivor annuity, mortality rates, survival probabilities, actuarial valuation, actuarial present value, life annuity, multiple-life annuity, annuity benefits, life tables, mortality assumptions, annuity factors, insurance liabilities, actuarial modelling.