construction of the german annuity table dav 2004 r dr. ralf krüger

Construction of the German Annuity TableDAV 2004 R

Dr. Ralf Krüger

2Dr. Ralf Krüger – DAV 2004 R

Introduction

Construction of DAV 2004 R

Base tables

Mortality projections

International Comparisons

Introduction


Base tables



Agenda


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!


Life expectancy at birth (both sexes)

64

46

69

69

69

68

6688

44

84

84

83

83

82

J

L

D

UK

Ch

USA

RB

1950/55 2045/50Source: http://www.un.org/esa/population

Life expectancy at birth (both sexes)

J

L

D

UK

Ch

USA

RB

Longevity – International comparison


Life expectancy at birth Census data

20

40

60

80

1870 1905 1940 1975 2010Year

Females

Males

36

39

76

82

Longevity - Germany


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


Mortality tables

Valuation tables also used for pricing purposes

4th 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)


Starting point for DAV 2004 R (2)

population data

previous annuity table


Agenda

Introduction


Base tables




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


Agenda

Introduction


Base tables




Payout period

Enough data for ages 60 - 99

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


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


Selection effect

Males 67% 88% 100%Females 71% 80% 100%

Males

Females


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


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


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

Lz reserve of insured persons aged z in the model portfolio

Tz random variable of the released reserve of deaths aged z within a

year

z z z z zP( T (1 s) L q ) 95%Σ Σ

Risk of random fluctuation


Mortality rates - Year 1999payout beginning at 65

0,00001

0,0001

0,001

0,01

0,1

1

0 20 40 60 80 100 120

Age

ln(q(z))

Males

Females

Base mortality table

Selection period

Deferment period Payout period


Agenda

Introduction


Base tables




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


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


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


Mortality rates - Males German census data

-7

-5

-3

-1

1870 1910 1950 1990Year

ln(qx)

80

60

40

Attained age model – description (1)


Mortality rates - Females German census data

-7

-5

-3

-1

1870 1910 1950 1990Year

ln(qy)

80

60

40




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


q(z,t) mortality rate for a person aged z in calendar year t

exp(–F(z)) annual decrease factor

t0 base year

Attained age model – formula (1)

q(z,t) = q(z,t0) * exp(–F(z) * (t – t0))

q(z,t0)

q(z,t)

timet0 t


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


Population mortality trends


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%


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


Linear trend reduction

Initial trend(short-term level)

Target trend(75% of medium-term level)


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


Annual mortality decrease DAV 2004 R

0%

1%

2%

3%

4%

0 20 40 60 80 100 120Age

F(z)

Males

Females

Projection of the mortality trend


Effect of mortality decrease

Males Females

Year of birth 1960 1970 1980 1960 1970 1980

Age 0 87 90 93 93 95 97

Age 40 50 52 54 55 57 58

Age 60 32 34 36 36 38 39

Age 80 15 16 18 18 19 21

Remaining life expectancies according to DAV 2004 R


Summary

Population

Base tables 1999 Trend function

DAV 2004 R

Level parameter risk

Risk of random fluctuation

Model risk

Trend parameter risk

Portfolio


Agenda

Introduction


Base tables




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



Annual mortality decrease 2006 - Males

0%

1%

2%

3%

4%

50 60 70 80 90 100Age

Germany DAV 2004 R

Switzerland ER 2000

Austria AVÖ 2005RUK IA 92 mc



Annual mortality decrease 2006 - Females

0%

1%

2%

3%

4%

50 60 70 80 90 100Age

Germany DAV 2004 R

Switzerland ER 2000

Austria AVÖ 2005RUK IA 92 mc


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)

Ch D A UK B

ER 2000 DAV 2004 R AVÖ 2005 R IA 92 mc

MRFR1992

(incl. age

shift)

Males 104% 100% 100% 97% 94%

Females 102% 100% 98% 96% 96%


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)

Ch D A UK B

ER 2000 DAV 2004 R AVÖ 2005 R IA 92 mc

MRFR1992

(incl. age

shift)

Males 105% 100% 97% 93% 85%

Females 100% 100% 97% 93% 89%


Jeanne Calment (1875–1997)


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.

Thank you for your interest.

Dr. Ralf Krüger

construction of the german annuity table dav 2004 r dr. ralf krüger

Documents

ralf krger dav

ralf krger slide

r payout period

r selection reasons

r jeanne calment

german annuity table

r growing market

r longevity germany