[discount_rates_problem] [background]

What do I mean by discounting? Ignoring tax, if we knew for certain that we would earn interest at the rate of 3 % pa for as long as we needed, then 103 due in a year's time could be financed by a capital sum of 100; that is all discounting is! However secure such a financial environment might appear, we don't live there.

We have no certainty, we may need to deal with much longer periods and the assets available may be quite different to cash deposits. Discounting is no longer the sole province of actuaries, who need to bring something else to the table in order to add value. In fact, the future is, and always has been, unknowable so that no uniquely correct interest rate can be determined in advance, which needs to be recognised far more than has been common. Instead of trying to select something which doesn't exist, we should be looking at stochastic processes, which is what I'll be doing here.

As a process, discounting has been with us for a very long time. When I was a trainee, the UK actuaries' standard textbook was “Compound Interest and Annuities Certain” by DWA Donald (1970) but many others have been written. Around 12 years ago, the Institute and Faculty of Actuaries conducted a wide-ranging discount rates framework exercise. The first part was a discussion paper in 2010 by Daykin and Patel, who provided a brief history in section 3, which is worth reading. The working party delivered their final paper in 2011. Discussions were held in London and Edinburgh.

Actuaries used to define the discount rate, “d”, as “iv”. However, in common parlance, I'm looking at the “interest rate” to be used for discounting future cashflows. The term “MtM” is used to represent “mark to market” and “Off” is used to represent “off market”, to be defined in some other manner (yet to be determined). Elsewhere, I have used “DV” but that doesn't fully convey the point of not being marked to market. We also need to think about long-term entities.