Actuarial Valuation of Pension and Gratuity Defined Benefit Plans

In this introductory short course on actuarial valuations we introduce commutation functions, the actuarial valuation process flow followed by a simple valuation example and a brief walk through the IAS 19 employee benefit valuation disclosure format.

Lesson one begins with commutation function.

While Life contingencies course and literature moved towards a continuous valuation framework, discrete commutation function remain the mainstay of actuarial work. A commutation function is summarized result extracted from actuarial tables to estimate probability of death (mortality), illness (morbidity), termination and withdrawal (turnover) from the underlying population. In the pre-calculator world commutation functions and tables were like statistical tables that helped move calculations faster. With the arrivals of electronic spreadsheets they became even more valuable calculations tools.

We first look at how commutation functions are developed:

And provide some examples of how commutation functions are used to determine the value of simple annuity and life insurance products and their premiums under deterministic assumptions of survival and constant & level rates of return:

These functions also aid the determination of actuarial liability and current service cost of post employment defined benefit plans by providing an easy way of present valuing, PV-ing,  benefit payments.

Our next posts address the Actuarial Valuation of Post-Employment Benefits, where we first consider the general process flow of valuing defined benefit gratuity and pension plans. The focus is on the sequence of steps and data requirements for the valuation to be completed.

This is followed by an example illustrating the valuation of actuarial liability and normal cost for a single employee’s benefit in a simplified gratuity defined benefit plan:

We also review an illustration of how IAS 19 disclosures are prepared:

And includes an example of how sensitivity analysis of key assumptions is carried out:

Leave a Comment