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Construction of the German Annuity Table DAV 2004 R Dr. Ralf Krüger

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2 Dr. Ralf Krüger – DAV 2004 R Introduction Construction of DAV 2004 R Base tables Mortality projections International Comparisons Introduction Construction of DAV 2004 R Base tables Mortality projections International Comparisons Agenda

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3 Dr. Ralf Krüger – DAV 2004 R Jeanne Calment (1875–1997) Sold her house to a 46-year-old notary for an annuity when she was 90 The buyer died at the age of 77 Jeanne Calment survived him and became the oldest person of the world. She died at the age of 122!

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4 Dr. Ralf Krüger – DAV 2004 R Longevity – International comparison

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5 Dr. Ralf Krüger – DAV 2004 R Longevity - Germany

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6 Dr. Ralf Krüger – DAV 2004 R Growing market 46% of premiums of new business (2003) Number of policies in force: 5% (1996) 16% (2003) Two basic product concepts Immediate annuities Deferred annuities (often including guaranteed annuity rates at outset and lump-sum payment option) The German annuity market

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7 Dr. Ralf Krüger – DAV 2004 R Mortality tables Valuation tables also used for pricing purposes 4 th German annuity valuation table since the 1950s Data sources Munich Re’s and Gen Re’s data pools (13.7 million years’ exposure) Population mortality tables Data from social insurance Starting point for DAV 2004 R (1)

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8 Dr. Ralf Krüger – DAV 2004 R Starting point for DAV 2004 R (2) population data previous annuity table

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9 Dr. Ralf Krüger – DAV 2004 R Agenda Introduction Construction of DAV 2004 R Base tables Mortality projections International Comparisons

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10 Dr. Ralf Krüger – DAV 2004 R Base tables Insured lives mortality in 1999 weighted by amounts Separate tables for deferment and payout period Trend Appropriate model Stronger for upper socio-economic group Safety margins Two-dimensional approach

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11 Dr. Ralf Krüger – DAV 2004 R Agenda Introduction Construction of DAV 2004 R Base tables Mortality projections International Comparisons

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12 Dr. Ralf Krüger – DAV 2004 R Payout period Enough data for ages Selection effect: see extra slides Extrapolation to ages 59- using population mortality rates Extrapolation to ages 100+: see extra slide Deferment period Enough data for ages 65- Extrapolation to ages 65+ using mortality rates of payout period Base tables

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13 Dr. Ralf Krüger – DAV 2004 R Selection Reasons for selection Annuities bought mainly from people who consider themselves to be healthy and long-lived Self-selection worsened by the lump-sum payment option Higher socio-economic status = lower mortality Main client group for annuities are people with above-average socio- economic status

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14 Dr. Ralf Krüger – DAV 2004 R Selection effect Males67%88%100% Females71%80%100% Males Females

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15 Dr. Ralf Krüger – DAV 2004 R Insured lives data insufficient No population data available Following the method in [TKV], we examine six approaches: Fit all six models to the actual mortality rates at ages 85 to 95 Assess accuracy of the models at ages 96 to 99 Evaluate extrapolation Compare with data from Japan [TKV] - Thatcher, Kannisto, Vaupel: The force of mortality at Ages 80 to 120 Extrapolation for ages 100+ Logistic model used for extrapolation

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16 Dr. Ralf Krüger – DAV 2004 R Margin for level parameter risk Differences between the observed and actual portfolio (structure, mortality level) Structural differences between observed portfolio and future new business Statistical fluctuation of the observed portfolio Reduction by 10% Margin for risk of random fluctuation Protection against a maximum loss at a defined prognosis level 6.3% (males) and 7.2% (females) Safety margins for the base tables

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17 Dr. Ralf Krüger – DAV 2004 R Reduction s for the risk of random fluctuation based on a model portfolio of 100,000 males resp. females with an age distribution typical for a German insurance portfolio so that where L z reserve of insured persons aged z in the model portfolio T z random variable of the released reserve of deaths aged z within a year Risk of random fluctuation

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18 Dr. Ralf Krüger – DAV 2004 R Base mortality table Selection period Deferment periodPayout period

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19 Dr. Ralf Krüger – DAV 2004 R Agenda Introduction Construction of DAV 2004 R Base tables Mortality projections International Comparisons

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20 Dr. Ralf Krüger – DAV 2004 R Models (1) Mortality decrease in the past due to Medical reasons Changes in nutrition Better hygiene Changes in style of living Improvement in general living conditions Nobody knows future mortality exactly Attained age model mostly used

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21 Dr. Ralf Krüger – DAV 2004 R Models (2) Attained age model Trend F(x) dependant on attained age x q(x,t+1)/q(x,t) = exp(-F(x)) Cohort model Trend G(t+1-x) dependant on cohort t+1-x q(x,t+1)/q(x,t) = exp(-G(t+1-x)) Synthesis model Combination of attained age and cohort model

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22 Dr. Ralf Krüger – DAV 2004 R Models (3) Likelihood ratio test: Synthesis model is the best for modeling German population data of the past However synthesis model not suitable for projecting mortality to the future Trend of cohort model for late cohorts increasingly uncertain Attained age model chosen for projecting mortality

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23 Dr. Ralf Krüger – DAV 2004 R Attained age model – description (1)

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24 Dr. Ralf Krüger – DAV 2004 R Attained age model – description (2)

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25 Dr. Ralf Krüger – DAV 2004 R Attained age model – description (3) Assumptions Mortality decrease depends on sex Mortality decrease depends on attained age The percentage of annual mortality decrease for fixed attained age and fixed sex is time-independent

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26 Dr. Ralf Krüger – DAV 2004 R q(z,t)mortality rate for a person aged z in calendar year t exp(–F(z))annual decrease factor t 0 base year Attained age model – formula (1) q(z,t) = q(z,t 0 ) * exp(–F(z) * (t – t 0 )) q(z,t 0 ) q(z,t) time t0t0 t

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27 Dr. Ralf Krüger – DAV 2004 R Projection of the mortality trend Trend function F(z) Estimated by using linear regression for ln(q(z,t)) = –F(z) * t + B(z) Based on method of least squares West German population trends are considered: Short-term: based on 10 tables 1989/91 to 1998/2000 Medium-term: based on 28 tables 1971/73 to 1998/2000 Long-term: based on 12 tables 1871/80 to 1998/2000

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28 Dr. Ralf Krüger – DAV 2004 R Population mortality trends

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29 Dr. Ralf Krüger – DAV 2004 R Trend loading for insured persons Various international studies have shown: Mortality decrease of insured persons greater than mortality decrease of the population Mortality decrease of upper socio-economic groups greater than mortality decrease of lower socio-economic groups Loading for insured persons: Increase in annual mortality decrease of 0.2%

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30 Dr. Ralf Krüger – DAV 2004 R Trend extrapolation for ages 90+ Based on data from Japan: Annual mortality decrease of 1% for ages ≥ 100 Annual mortality decrease in transition age band 90 to 99 defined by suitable quadratic polynomial

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31 Dr. Ralf Krüger – DAV 2004 R Linear trend reduction Initial trend (short-term level) Target trend (75% of medium- term level)

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32 Dr. Ralf Krüger – DAV 2004 R Safety margins for the trend Margin for model risk Mortality decrease will not decline in the future No trend reduction Margin for trend parameter risk Risk of an increase in the mortality improvement trend Additional 0.25% annual mortality decrease for all ages

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33 Dr. Ralf Krüger – DAV 2004 R Projection of the mortality trend

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34 Dr. Ralf Krüger – DAV 2004 R Effect of mortality decrease MalesFemales Year of birth Age Age Age Age Remaining life expectancies according to DAV 2004 R

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35 Dr. Ralf Krüger – DAV 2004 R Summary Population Base tables 1999Trend function DAV 2004 R Level parameter risk Risk of random fluctuation Model risk Trend parameter risk Portfolio

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36 Dr. Ralf Krüger – DAV 2004 R Agenda Introduction Construction of DAV 2004 R Base tables Mortality projections International Comparisons

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37 Dr. Ralf Krüger – DAV 2004 R International comparisons - trends Annuity tables with mortality decrease projection for whole future (q(x,t+1)/q(x,t) < 1 for all future t): Switzerland: ER 2000 UK: IA 92 mc Austria: AVÖ 2005 R Swiss table without trend reduction UK and Austrian table with trend reduction

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38 Dr. Ralf Krüger – DAV 2004 R International comparisons - trends

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39 Dr. Ralf Krüger – DAV 2004 R International comparisons - trends

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40 Dr. Ralf Krüger – DAV 2004 R International comparisons – premiums (1) Immediate annuity Payment beginning of year Age 60 Interest rate 2.75% Year of birth 1945 Net single premiums (in % of DAV 2004 R) ChDAUKB ER 2000DAV 2004 RAVÖ 2005 RIA 92 mc MRFR1992 (incl. age shift) Males104%100% 97%94% Females102%100%98%96%

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41 Dr. Ralf Krüger – DAV 2004 R International comparisons – premiums (2) Deferred annuity Deferment period 20 years Age 40 Payment beginning of year Year of birth 1965 Interest rate 2.75% Net single premiums (in % of DAV 2004 R) ChDAUKB ER 2000DAV 2004 RAVÖ 2005 RIA 92 mc MRFR1992 (incl. age shift) Males105%100%97%93%85% Females100% 97%93%89%

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42 Dr. Ralf Krüger – DAV 2004 R Jeanne Calment (1875–1997)

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43 Dr. Ralf Krüger – DAV 2004 R Acknowledgements The new German annuity valuation table DAV 2004 R was derived by a DAV committee consisting of Holger Bartel, Marcus Bauer, Bärbel Michaeli, Werner Mörtlbauer, Eberhard Münzmay, Gabriele Nagel, Kornelia Nolle, Catherine Pallenberg, Ulrich Pasdika, Volker Priebe, Michael Rösgen, Esther U. Schütz and Jürgen Wolff. Without the substantial contributions made by every single member of the committee the new table would not have come into being. We are also grateful for the guidance of the steering committee, the “DAV-Arbeitsgruppe Biometrische Rechnungsgrundlagen”. Parts of this presentation were previously published in a paper, "Coping with Longevity—The New German Annuity Valuation Table” by Ulrich Pasdika and Jürgen Wolff. Copyright 2005 by the Society of Actuaries, Schaumburg, Illinois. Reprinted with permission.

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Thank you for your interest. Dr. Ralf Krüger

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