Alternative approaches for unwinding the discount - with particular focus on determining interest co

Speaker: Alf Gohdes

Probably one of the most basic tools applied in actuarial work is that of discounting payments due in the future to compute a present value of such future payments, thereby taking into account the time value of money. The reverse process is also commonly applied, namely that of accumulating present values and/or amounts payable in future to some further point in time. The understanding of such processes is engrained in the training of all actuaries since they are typically applied as a matter of course in the everyday work of an actuary.

Until recently, not much appears to have been written in actuarial literature about the unwinding of the discount of present values i.e. how the present value is adjusted by the time value of money from the beginning of a time period to its end. This is of particular practical relevance in employers' accounting for pension cost when a yield curve and not a single rate is used for discounting. Different approaches can lead to significantly different results.

The aim of the paper is to systematically consider the issue of discounting and its unwinding. First, the theory underlying discounting is summarised. Next, an analysis of different approaches to unwinding including their justification is performed, including a review of expectations theory. In addition, the practical implications of each approach under US-GAAP and IFRS accounting standards are then compared in numerical examples. Finally, an attempt is made to express an opinion on the relative merits of the different approaches from both a theoretical and a practical point of view.