1. Projecting future change in the Mortality Rates is not only a Statistical Exercise Henk van Broekhoven

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

3. Development life expectancy

5. Some other countries

6. 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 can’t be that ….)

7. Why we underestimate longevity risk? An perhaps even more important part of the model is the uncertainty In 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 developments –Medical development can lead to a shock in the life expectancy, above the modelled random walk –A kind of extreme event!

8. An alternative model A 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

9. Long term trend versus short term trend Last observation year e(x)

10. Long term trend versus short term trend Last observation year e(x)

11. The Model The 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 analysis –The 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..

12. The goal table Based 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)

13. The goal table Based on expert opinion –As 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 don’t use something like goal tables.

14. The goal table Based on expert opinion (2) –Sometimes also experts can help with “uncertainty” in the goal table –Problem: talking to 5 experts will end up in 6 opinions. Still, even if you don’t use expert opinion, always compare your own results with the ideas of the experts

15. Correlations mortality development

16. Goal table As you can see there are high correlations between countries within one region –Why 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.

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

18. The Model With: –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)

19. The Model Normally (in simple continuation of observed trend) Making the f(x) time dependent (f(x;t)):

20. The Model Define: 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:

21. The Model Explanation : When t increases the third factor will dominate the middle factor So the local trend (f(x;j)) will become less important as the time goes on

22. The Model Solving  (x) :

23. The Model Possible extra conditions:

24. Impact short-long trend modelling For the new Dutch prognosis model we used this model: –Short trend based on 2001-2008 –Long trend based on 1988-2008 –Goal table based on long trend, year 2060 –Next sheet impact for old age pension combined with 70% widows pension at some ages

25. Impact short-long trend modelling for NL Last observation year e(x) Age OP(65) OP+70%WP 25+1.0% +0.2% 45+3.7% +2.0% 65 +3.6% +2.6%

26. Uncertainty shocks Living 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 table Expert opinion: CBS (Dutch official statistical office) that the uncertainty in the future life expectancy (2050) means that 1 standard deviation equals 3.2 years.

27. Some conclusions Longevity 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!