The ins and outs of bulk annuities

The UK has a well developed and highly competitive market in bulk annuities. These typically arise when a defined-benefit pension scheme wants to insure its liabilities. The most obvious scenario is when a pension scheme is being wound up and benefits have to be secured with an insurance company.  Since the pension scheme is ceasing to exist, individual policies are purchased for each member. The now-former pension-scheme member owns his or her own annuity policy, which cannot be surrendered or transferred once annuity payments start.  All risks such as longevity and investment are transferred to the insurer in a transaction known as a buy-out.

However, there is another option called a buy-in — the scheme continues to exist and pay pensions, but with a single insurance policy covering the risks from many pensioners.  Here the policy is owned by the pension scheme, not the individual members, and the pension scheme then acts as a conduit for payments from the insurer to the pensioners.  As with the buy-out policy, the insurer bears the longevity and investment risks.

Both kinds of bulk annuity have their place, and each pension scheme will decide on its own strategy.  This includes partial buy-outs or buy-ins, i.e. covering only part of the scheme's liabilities, although there are some points to beware about selective buy-outs based on health.  However, buy-ins throw up some interesting challenges for an insurer's mortality investigations.  Buy-outs are like ordinary annuities — once payment starts, the only event which can happen to the policy is mortality.  With only one mode of exit, this leads to what actuaries call a single decrement analysis, and it can be done using either the force of mortality, μ_x, or the rate of mortality, q_x.  In contrast, buy-ins are additionally at risk of surrender or transfer: it can and does happen that the owning pension scheme wants to cancel the policy.  This complicates mortality analysis involving buy-in annuities, as they are obviously at risk of two competing decrements: mortality and transfer.

Analysing mortality when there are competing decrements is problematic for a q_x-style investigation.  For this reason, analysts performing a q_x-style analysis will sometimes just exclude the data for buy-in annuities.  This is far from satisfactory, however, as ignoring data is an inefficient use of available resources.  However, additional assumptions have to be made if buy-in annuities are to be included in a q_x model.  These assumptions are not always realistic, but they will always complicate the mathematics and sometimes cause errors.

Fortunately, there is a simple solution to including buy-in annuities in the mortality investigation: use a survival model for the force of mortality, μ_x.  For a mortality study, the surrender of a buy-in policy is simply a kind of censoring (the surrender event is unrelated to an individual's risk of mortality, so it is called uninformative censoring).  This has no impact on the model structure for μ_x-style analysis, whereas two or more decrements cause headaches for q_x models.  In addition, survival models easily handle fractional years of exposure. By allowing a bulk-annuity insurer to use all of its available information, survival models deliver clear business benefits over q_x-style analysis.