9.1 Simulating the value of the liabilities The best-estimate value of the liabilities can be obtained by assuming that future mortality probabilities will develop according to the model comparisons in Appendix A, whereby all disturbances are set at nil. It is also possible to simulate scenarios in which the disturbances are generated stochastically by means of a multivariate normal distribution. Table 12 gives as an example for 10,000 such scenarios the average and the quantiles for 95%, 97.5% and 99.5% for the Pension Liabilities Provision. For this purpose, the average model portfolios comprising men and women are used with a fixed actuarial discount rate of 3% and 1%. The outcomes are expressed relative to the best-estimate values. Outcomes of the simulation for the provision for pension liabilities (in relation to the best estimate) - 3% interest RP Standard deviation Quantiles 50% 95% 97.5% 99.5% 2.2% 100.0% 103.6% 104.2% 105.4% Men SP 1.6% 100.0% 102.6% 103.2% 104.2% RP + SP 1.3% 100.0% 102.2% 102.5% 103.3% RP 1.5% 100.0% 102.5% 102.9% 103.9% Women SP 2.0% 100.0% 103.3% 104.0% 105.3% RP + SP 1.3% 100.0% 102.1% 102.5% 103.3% Table 12 Results of the simulation of provisions based on 3% for model portfolios (men and women averaged) ■ RP = retirement pension SP = survivor’s pension In the case of a 1% actuarial discount rate, the distribution in the results is greater. Results of the simulation of provisions based on 1% for model portfolios (men and women averaged) RP Standard deviation Quantiles 50% 95% 97.5% 99.5% 2.7% 100.0% 104.4% 105.2% 106.7% Men SP 1.8% 100.0% 102.9% 103.6% 104.7% RP + SP 1.7% 100.0% 102.7% 103.2% 104.2% RP 1.9% 100.0% 103.1% 103.6% 104.7% Women SP 2.6% 100.0% 104.3% 105.2% 107.0% RP + SP 1.7% 100.0% 102.7% 103.2% 104.2% Table 13 Results of the simulation of provisions based on 1% for model portfolios (men and women averaged) ■ RP = retirement pension SP = survivor’s pension The distribution resulting from the simulations strongly resembles a normal distribution. As is apparent from the above tables, the spread of the various types of pensions is considerably higher, in particular in the case of the retirement pension for men and the survivor’s pension for women. Simulations based on Projection Table AG2014 show a comparable distribution for the retirement pension, but the survivor’s pension results in a much higher standard deviation: in the case of an actuarial discount rate of 3%, this is equal to 3.4% in the case of AG2014, as compared to 1.6% in the case of AG2016. This considerable reduction relates to the inclusion of the correlation between the mortality of men and women in the AG2016 model. Projection Table AG2016 Applications of the model 27
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