Projecting future change in the Mortality Rates is not only a Statistical ExerciseHenk van Broekhoven

What can you expect?Longevity risk often underestimated. Why?Input of expert opinionsExtreme events in longevity riskLong term estimates and short term estimates: longevity risk it is not only based the expectations in 2050 or 2060International comparison: correlation between countries/regions

Development life expectancy

Development life expectancy

Some other countries

Why we underestimate longevity risk?Most popular models in use are based on an almost linear extrapolation of a long term trend (e.g. the standard Lee Carter, or a simple extrapolation of a trend)The increasing increase of the life expectancy we see in most western countries in the last couple of years leads in to year by year adjustments in the same direction (projected first years in the model result every time in lower life expectancies than the real observations)Also sometimes the models are set up too conservative (it cant be that .)

Why we underestimate longevity risk?An perhaps even more important part of the model is the uncertaintyIn stochastic models like Lee Carter the uncertainty is based on the volatility (random walk) of the delta like showed in the graph.But there is more: uncertainty because of medical developmentsMedical development can lead to a shock in the life expectancy, above the modelled random walkA kind of extreme event!

An alternative modelA solution of the problems can be to distinguish between a short term trend and a long term trend and to combine both in a model.The short term trend can be based on recent observed mortality developments (last 5 to 10 years)The long term trend can be based on:Estimation via a longer history (e.g. >20 years)Expert opinion about future life expectancy (e.g. 2050 or 2060)International comparison

Long term trend versus short term trendLast observation yeare(x)

Long term trend versus short term trendLast observation yeare(x)

The ModelThe idea is to let the mortality rates in the future grow to a goal table, but start with the recent observed trend

The goal table can be based the observed long term trend, on expert opinion and / or average mortality in a group of comparable countries

This goal table model can also be used in case for some (developing) countries not enough data is available to make detailed trend analysisThe goal table can be based on prognosis in comparable countries or expert opinions and for the model only limited information is needed wrt local trends. .

The goal tableBased on a long term trend. The goal table can be based on one of the existing models like Lee Carter or continuation of historical trends over a longer period (e.g. > 20 years)

The goal tableBased on expert opinionAs in the title of this presentation you can see that in my opinion statistics and historical data can not be the only source of a good prognosis model.We as actuaries need input from experts from other disciplines, like medical and demographic experts.I think this should be always the case, also when you dont use something like goal tables.

The goal tableBased on expert opinion (2)Sometimes also experts can help with uncertainty in the goal tableProblem: talking to 5 experts will end up in 6 opinions.

Still, even if you dont use expert opinion, always compare your own results with the ideas of the experts

Correlations mortality development

Goal tableAs you can see there are high correlations between countries within one regionWhy not one goal table for the whole region?Countries with higher mortality but steeper trends can use a goal table based on another region (e.g. Central Europe compared to Western Europe) Take care of the structure of the mortality tables Countries with a lack of data can make use of this.

Short term trendCan be based on the local trend observed in the last 5 to 10 years.

The ModelWith:q(x;j) = last observed mortality rate in the year j. f(x;j) = observed local trend over the last 5 to 10 years q(x;j+t) = mortality rate from the goal table (e.g. j+t = 2060)

The ModelNormally (in simple continuation of observed trend)

Making the f(x) time dependent (f(x;t)):

The ModelDefine: f(x;j) is the local trend (can be based on a Lee-Carter estimation or simply a continuation of the recent trend) and

So

And:

The ModelExplanation:

When t increases the third factor will dominate the middle factorSo the local trend (f(x;j)) will become less important as the time goes on

The ModelSolving (x) :

The ModelPossible extra conditions:

Impact short-long trend modellingFor the new Dutch prognosis model we used this model:Short trend based on 2001-2008Long trend based on 1988-2008Goal table based on long trend, year 2060

Next sheet impact for old age pension combined with 70% widows pension at some ages

Impact short-long trend modelling for NLLast observation yeare(x)Age OP(65) OP+70%WP +1.0% +0.2%+3.7% +2.0%65 +3.6% +2.6%

Uncertainty shocksLiving 1 year longer in 2060 (based on estimated e(0) means for a deferred annuity:X=25 +2.7%X=45 +1.6%X=65 +0.4%This can be calculated by simply adjusting the goal tableExpert opinion: CBS (Dutch official statistical office) that the uncertainty in the future life expectancy (2050) means that 1 standard deviation equals 3.2 years.

Some conclusionsLongevity risk is not only based on the long term trend but also:Uncertainty (shock scenario)Short term trend for the at the moment older part of the portfolio.

Without expert opinion we can not create good models!