There are several ways of looking at longevity trend risk, as covered in our recent seminar. However, regardless of how you choose to look at this risk, there are some pitfalls to watch out for. By way of illustration, we will consider here the capital requirements under the stressed-trend approach to longevity risk, although the basic points apply to most approaches.

Figure 1 shows the capital requirements implied by stressing the longevity trend over the lifetime of the annuitant. This is the so-called run-off approach, as opposed to the one-year, value-at-risk approach required by Solvency II (or ICA in the United Kingdom). The first aspect of Figure 1 is how different the various capital requirements are…

The Society of Actuaries (SOA) in North America recently published an exposure draft of a proposed interim mortality-improvement basis for pension-scheme work. The new basis will be called "Scale BB" and is intended as an interim replacement for "Scale AA".   Like Scale AA, the interim Scale BB is one-dimensional in age, i.e. mortality improvements vary by age and gender only. However, the SOA is putting North American actuaries on notice that a move to a two-dimensional projection is on the cards:

We previously ran a seminar on stochastic projection models for longevity risk. Our follow-up seminar focuses on specific aspects of ICAs and Solvency II.  The seminar contains four presentations:

1. Improving the Lee-Carter model using smoothing techniques (Iain Currie).
2. Issues with parameter correlations, illustrated by the APC model (Iain Currie).
3. Testing the robustness of an internal model before committing to using it (Gavin Ritchie).
4. A value-at-risk (VaR) framework for longevity trend risk (Stephen Richards).

The slide packs can be downloaded from the panel on the right.

It is fairly obvious by now that we are strong advocates for stochastic projection models. Such models crucially provide a basis with two components - a best-estimate force of mortality by age and year, and matching standard error values for the same 2D range. Not all bases derive from stochastic methods of course, and so called deterministic bases will produce a single estimate without uncertainty measures. A popular example of a deterministic basis in use is that from the CMI, which is updated each year in response to revised data from the ONS and is driven by a user-input expectation of the long-term mortality improvement rate.

Both types of basis are in common usage and are often applied in concert. One example…

A while back I wrote about the lower life expectancy in Scotland. This has a number of drivers, but poor diet is one of them. In the same blog I made a reference to the nutritional abomination that is the deep-fried Mars bar.  One of our London-based clients confessed that he thought this was a myth made up and propagated by the media. Sadly, I can confirm that it is no myth, as evidenced by the picture I took this weekend of a sign in a cafe window in Broughton Street, Edinburgh:

You might think this is bad enough. However, the same cafe also offers a topical alternative to its patrons:

We wish all our readers a relaxing Easter break. Preferably without deep-fried confectionery.

I'm giving away rather too much information about my age when I say I started work in 1990 right after graduating from university.   Not long into my first job at a UK insurer, I was called to a meeting of the actuarial department.  At this meeting was a man with the job title of Research Actuary.  During the meeting he suggested that our employer's investment strategy should be set such as to target a "fixed probability of ruin".   The idea was to accept that insolvency was always a possibility, but to recognise this and pick the assets - and the business strategy - to match the liabilities to make sure this possibility was suitably unlikely.  As I was fresh out of university, I couldn't imagine running…

Longevity trend risk is different from most other risks an insurer faces because the risk lies in the long-term trajectory taken by mortality rates. This trend unfolds over many years as an accumulation of small changes, so a natural approach is to calculate reserves using a long-term stress projection from a stochastic model, as shown in Figure 1.

Figure 1. Central projection from a Lee-Carter model, together with the lower 99.5th confidence level derived from multiplying the projection standard error by Z=-2.58 (this being the lower 99.5th point of the N(0,1) distribution).

The stressed-trend approach behind Figure 1 can be used for a variety of models - Table 1 shows the best-estimate and 99.5th percentile…

If you'll forgive the nautical metaphor, forecasting longevity over the past few decades has proven to be anything but plain sailing. Those plotting a course with unshakable certainty have usually ended up storm-tossed and floating in a barrel. Since the future is unknowable, any methodology applied to forecasting must have uncertainty at its heart, which is why we advocate using stochastic projection models (and more than one at that).

Stochastic projection models are tricky beasts, however, with many methods of forecasting (ARIMA time series, drift models, penalty projections, bivariate projections, and others), each with different characteristics. One concern that arises from this sophistication…

In an earlier post we looked at the implications for savers of the historically low interest rates in the UK.  Low interest rates are a policy response to the unusual economic conditions in which the developed world currently finds itself.  Besides being bad for savers, low interest rates increase the value of liabilities for pension schemes and can thus aggravate pension deficits.

However, these record low interest rates only apply in the short term, with a steep rise to a more normal longer-term rate.  This is shown in Figure 1, which plots the redemption yields for UK government gilts on 16th December 2011.  The points appear to follow a smooth underlying pattern, known as the yield curve.

Figure 1. Redemption…

The CMI recently asked for an overview note on survival models.  Since this subject is of wider actuarial interest, we wanted to make this publically available. An electronic copy can be downloaded from the link on the right.