Summary

In this chapter we derive expressions for the valuation and analysis of life contingent annuities. We consider benefit valuation for different payment frequencies, and we relate the valuation of annuity benefits to the valuation of the related insurance benefits.

We consider how to calculate annuity valuation functions. If full survival model information is available, then the calculation can be exact for benefits payable at discrete time points, and as exact as required, using numerical integration, for benefits payable continuously. Where we are calculating benefits payable more frequently than annual (monthly or weekly, say) using only an integer age life table, a very common situation in practice, then some approximation is required. We derive several commonly used approximations, using the UDD assumption and Woolhouse's formula, and explore their accuracy numerically.

Introduction

We use the term life annuity to refer to a series of payments to (or from) an individual as long as the individual is alive on the payment date. The payments are normally made at regular intervals and the most common situation is that the payments are of the same amount. The valuation of annuities is important as annuities appear in the calculation of premiums (see Chapter 6), policy values (see Chapter 7) and pension benefits (see Chapter 9).