Innovation in life insurance products: Special-rate annuities E. Pitacco 1
1
D. Y. Tabakova2
MIB Trieste School of Management and DEAMS University of Trieste, ermanno.pitacco@mib.edu 2
MIB Trieste School of Management and Area Science Park, daniela.tabakova@mib.edu
DemoLab November 19, 2020
Agenda 1
Introduction and motivation
2
Innovation in life insurance product
3
Special-rate life annuities
4
Market issues
5
Biometric model
6
The actuarial model
7
Assessments of portfolios’ risk profile: Deterministic approach
8
Assessments of portfolios’ risk profile: Stochastic approach
9
Facing the annual payouts
10
Concluding remarks
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Introduction and motivation
• "Weak" features of traditional life annuity product (SPIA);
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Introduction and motivation
• "Weak" features of traditional life annuity product (SPIA); • How to design more attractive products (from customer perspective);
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Introduction and motivation
• "Weak" features of traditional life annuity product (SPIA); • How to design more attractive products (from customer perspective); • Looking at product developed in various markets =⇒ innovation in life annuity design.
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Agenda 1
Introduction and motivation
2
Innovation in life insurance product
3
Special-rate life annuities
4
Market issues
5
Biometric model
6
The actuarial model
7
Assessments of portfolios’ risk profile: Deterministic approach
8
Assessments of portfolios’ risk profile: Stochastic approach
9
Facing the annual payouts
10
Concluding remarks
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Innovation in life insurance product More benefits
More flexibility
SPIA
Linking benefits
Guarantee period Money-back Last-survivor ann. LTC uplift
• • • •
Income drawdown with GMWB
Investment-linked Longevity-linked
• •
Benefit restrictions
Better annuity rates
• •
Temporary life annuties Old-age life annuities
Special-rate life annuities
Figure 1: Generalizing the life annuity structure November 19, 2020
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Agenda 1
Introduction and motivation
2
Innovation in life insurance product
3
Special-rate life annuities
4
Market issues
5
Biometric model
6
The actuarial model
7
Assessments of portfolios’ risk profile: Deterministic approach
8
Assessments of portfolios’ risk profile: Stochastic approach
9
Facing the annual payouts
10
Concluding remarks
November 19, 2020
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Special-rate life annuities Purposes Potential annuitants
Figure 2: Potential annuitants population and standard annuity portfolio
Standard annuity portfolio
VERY GOOD
VERY BAD
Health conditions
Figure 3: Potential annuitants
Potential annuitants
population and (unrealistic) better-rate annuity portfolio
(Hypothetical) better-rate annuity portfolio
VERY GOOD
VERY BAD
Health conditions
Figure 4: Potential annuitants population and annuity portfolio also consisting of three special-rate annuity subportfolios
Potential annuitants Special-rate annuity sub-portfolios
Standard annuity sub-portfolio
VERY BAD
VERY GOOD
Health conditions November 19, 2020
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Special-rate life annuities
(cont’d)
Underwriting schemes UNDERWRITING
Type of rating factors
Number of rating factors
Number of rating classes
Disease
Single-class
Lifestyle
Multi-class
Environment
Individual underwriting
Figure 5: Approaches to underwriting for special-rate life annuities
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Agenda 1
Introduction and motivation
2
Innovation in life insurance product
3
Special-rate life annuities
4
Market issues
5
Biometric model
6
The actuarial model
7
Assessments of portfolios’ risk profile: Deterministic approach
8
Assessments of portfolios’ risk profile: Stochastic approach
9
Facing the annual payouts
10
Concluding remarks
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Market issues Supply and demand Figure 6: Development of special-rate annuity supply in the UK
Figure 7: The demand for special-rate annuities in the UK market; data from Towers Watson and Association of British Insurers
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Market issues
(cont’d)
Statistical data (1) Figure 8: All-cause annual death rates among men, US, by age, for diabetics and non-diabetics
Figure 9: Survival functions (from age 60) for smokers and non-smokers
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Market issues
(cont’d)
Statistical data (2) Figure 10: Age-distribution of deaths for males age 60
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Market issues
(cont’d)
Benefits Figure 11: Increase in the annuity benefit (on a monthly basis) for 65 year old with a 50,000 GBP fund (single premium), no guarantee period
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Agenda 1
Introduction and motivation
2
Innovation in life insurance product
3
Special-rate life annuities
4
Market issues
5
Biometric model
6
The actuarial model
7
Assessments of portfolios’ risk profile: Deterministic approach
8
Assessments of portfolios’ risk profile: Stochastic approach
9
Facing the annual payouts
10
Concluding remarks
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Biometric model
Figure 12: Curves of deaths for different life annuity sub-portfolios
Standard life annuities Enhanced life annuities Impaired life annuities
Age
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Agenda 1
Introduction and motivation
2
Innovation in life insurance product
3
Special-rate life annuities
4
Market issues
5
Biometric model
6
The actuarial model
7
Assessments of portfolios’ risk profile: Deterministic approach
8
Assessments of portfolios’ risk profile: Stochastic approach
9
Facing the annual payouts
10
Concluding remarks
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The actuarial model
• Portfolio structures:
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The actuarial model
• Portfolio structures: ◌ subportfolio SP1 initially consisting of n1 standard life annuities;
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The actuarial model
• Portfolio structures: ◦ subportfolio SP1 initially consisting of n1 standard life annuities; ◦ subportfolio SP2 initially consisting of n2 enhanced life annuities;
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The actuarial model
• Portfolio structures: ◦ subportfolio SP1 initially consisting of n1 standard life annuities; ◦ subportfolio SP2 initially consisting of n2 enhanced life annuities; ◦ subportfolio SP3 initially consisting of n3 impaired life annuities.
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The actuarial model
• Portfolio structures: ◦ subportfolio SP1 initially consisting of n1 standard life annuities; ◦ subportfolio SP2 initially consisting of n2 enhanced life annuities; ◦ subportfolio SP3 initially consisting of n3 impaired life annuities. • Quantities referred to:
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The actuarial model
• Portfolio structures: ◦ subportfolio SP1 initially consisting of n1 standard life annuities; ◦ subportfolio SP2 initially consisting of n2 enhanced life annuities; ◦ subportfolio SP3 initially consisting of n3 impaired life annuities. • Quantities referred to: ◦ Actuarial values;
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The actuarial model
• Portfolio structures: ◦ subportfolio SP1 initially consisting of n1 standard life annuities; ◦ subportfolio SP2 initially consisting of n2 enhanced life annuities; ◦ subportfolio SP3 initially consisting of n3 impaired life annuities. • Quantities referred to: ◦ Actuarial values; ◦ Risk index;
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The actuarial model
• Portfolio structures: ◦ subportfolio SP1 initially consisting of n1 standard life annuities; ◦ subportfolio SP2 initially consisting of n2 enhanced life annuities; ◦ subportfolio SP3 initially consisting of n3 impaired life annuities. • Quantities referred to: ◦ Actuarial values; ◦ Risk index; ◦ Cash flows;
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The actuarial model
• Portfolio structures: ◦ subportfolio SP1 initially consisting of n1 standard life annuities; ◦ subportfolio SP2 initially consisting of n2 enhanced life annuities; ◦ subportfolio SP3 initially consisting of n3 impaired life annuities. • Quantities referred to: ◦ Actuarial values; ◦ Risk index; ◦ Cash flows; ◦ Portfolio fund.
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Agenda 1
Introduction and motivation
2
Innovation in life insurance product
3
Special-rate life annuities
4
Market issues
5
Biometric model
6
The actuarial model
7
Assessments of portfolios’ risk profile: Deterministic approach
8
Assessments of portfolios’ risk profile: Stochastic approach
9
Facing the annual payouts
10
Concluding remarks
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Deterministic approach Biometric assumptions 100000 Impaired annuity Enhanced annuity Standard annuity
6000
4000
lx
dx
75000
2000
50000
Impaired annuity Enhanced annuity Standard annuity
25000
0
0 0
25
50
75
100
0
25
Age
50
75
100
Age
Figure 13: Life table
Figure 14: Life table
comparison: dx
comparison: lx
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Deterministic approach
(cont’d)
Impact of the portfolio structure (1) Figure 15: Cases 1.3 - impact of the
Portfolio
n2
n3
Ď (10 000, n2 , n3 )
portfolio structure on the risk index
P01 P02 P03 P04 P05 P06
500 600 700 800 900 1 000
250 300 350 400 450 500
0.002407197 0.002412496 0.002417448 0.002422070 0.002426375 0.002430381
Figure 16: Cases 1.3 - impact of
190000
the portfolio structure on the annual cash flows
Cases P01
180000
P02
Annual cash flows
P03 P04 P05 P06
170000
160000
150000
0
1
2
3
4
5
Policy anniversary November 19, 2020
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Deterministic approach
(cont’d)
Impact of the portfolio structure (2) Figure 17: Cases 1.4 - impact of the
Portfolio
n1
n2
n3
Ď (n1 , n2 , n3 )
portfolio structure on the risk index
P01 P02 P03 P04 P05 P06
9 750 9 700 9 650 9 600 9 550 9 500
500 600 700 800 900 1 000
250 300 350 400 450 500
0.002340041 0.002352541 0.002364783 0.002376774 0.002388521 0.002400030
Figure 18: Cases 1.4 - impact of Cases
180000
P01 P02 P03
Annual cash flows
the portfolio structure on the annual cash flows
P04 P05
170000
P06
160000
150000
0
1
2
3
4
5
Policy anniversary November 19, 2020
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Deterministic approach
(cont’d)
Impact of the lifetime distributions Figure 19: Three different assumptions on lifetime dispersion for enhanced annuities dx
7500
5000
2500
Enhanced (80,4) Enhanced (80,8) Enhanced (80,12)
0 0
25
50
75
100
Age
Figure 20: Cases 2.3 - impact of the lifetime distributions on the risk index
Portfolio
D2 = D3
Ď (10 000, 1 000, 500)
P01 P02 P03 P04 P05 P06 P07 P08 P09 P10
4 5 6 7 8 9 10 11 12 13
0.002360437 0.002366549 0.002373800 0.002382362 0.002392205 0.002403223 0.002415280 0.002428234 0.002441949 0.002456293
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Agenda 1
Introduction and motivation
2
Innovation in life insurance product
3
Special-rate life annuities
4
Market issues
5
Biometric model
6
The actuarial model
7
Assessments of portfolios’ risk profile: Deterministic approach
8
Assessments of portfolios’ risk profile: Stochastic approach
9
Facing the annual payouts
10
Concluding remarks
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Stochastic approach Impact of the portfolio structure (1) Distribution of the annual benefit payout at time t = 10
Distribution of the annual cash flow at time t = 10
Cases
0.50%
P01
Cases
P02
P01
P03
P02 P03
0.40%
Frequency
Frequency
2.00% 0.30%
0.20%
1.00% 0.10%
110000
108000
106000
10500
10000
Amounts
104000
0.00%
0.00%
Amounts
Figure 21: Cases 1.3 -
Figure 22: Cases 1.3 -
Empirical distributions at time 10 of the portfolio payout
Empirical distributions at time 10 of the portfolio fund
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Stochastic approach
(cont’d)
Impact of the portfolio structure (2) Distribution of the annual benefit payout at time t = 10
3.00%
Distribution of the annual cash flow at time t = 10
Cases Cases
P01
P01
P02
P02
P03
P03
0.40%
Frequency
Frequency
2.00%
0.20%
1.00%
117000
114000
111000
108000
10250
10000
9750
Amounts
105000
0.00%
0.00%
Amounts
Figure 23: Cases 1.4 -
Figure 24: Cases 1.4 -
Empirical distributions at time 10 of the portfolio payout
Empirical distributions at time 10 of the portfolio fund
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Stochastic approach
(cont’d)
Impact of the lifetime distributions (1) Distribution of the annual cash flow at time t = 10 Cases P01 P02
P05
P03 P04 P05
0.20%
Frequency
Frequency
Distribution of the annual benefit payout at time t = 10
P04
P03 Cases
0.10%
P01 P02 P03
P02
P04 P05
Amounts
107000
10100
106000
10000
105000
9900
104000
9800
103000
0.00%
P01
Amounts
Figure 25: Cases 2.2 -
Figure 26: Cases 2.2 -
Empirical distributions at times 10 of the portfolio payout
Empirical distributions at time 10 of the portfolio fund
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Stochastic approach
(cont’d)
Impact of the lifetime distributions (2) Distribution of the annual cash flow at time t = 5
Distribution of the annual cash flow at time t = 10
Cases
0.60%
Cases
P01
P01
P02
P02
P03
P03
P04
P04 P05
0.20%
Frequency
Frequency
P05
0.40%
0.10%
0.20%
Amounts
107000
106000
105000
104000
103000
146000
145000
144000
143000
0.00% 142000
0.00%
Amounts
Figure 27: Cases 2.2 -
Figure 28: Cases 2.2 -
Empirical distributions at times 5 of the portfolio fund
Empirical distributions at time 10 of the portfolio fund
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Agenda 1
Introduction and motivation
2
Innovation in life insurance product
3
Special-rate life annuities
4
Market issues
5
Biometric model
6
The actuarial model
7
Assessments of portfolios’ risk profile: Deterministic approach
8
Assessments of portfolios’ risk profile: Stochastic approach
9
Facing the annual payouts
10
Concluding remarks
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Facing the total annual payouts
Total annual benefits payout at time t = 1
Total annual benefits payout at time t = 5
Total annual benefits payout at time t = 10
0.061 0.0560 0.0590
0.059
Assets/EV
Assets/EV
Assets/EV
0.060 0.0585
0.0580
0.0558
0.0556
0.0575 0.058 0.0554 50%
60%
70%
80%
90%
50%
60%
70%
Percentile P01
P02
P03
80%
90%
50%
60%
70%
Percentile P04
Figure 29: Assets backing the liabilities / Expected value at time 1
P01
P02
P03
80%
90%
Percentile P04
Figure 30: Assets backing the liabilities / Expected value at time 5
P01
P02
P03
P04
Figure 31: Assets backing the liabilities / Expected value at time 10
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Agenda 1
Introduction and motivation
2
Innovation in life insurance product
3
Special-rate life annuities
4
Market issues
5
Biometric model
6
The actuarial model
7
Assessments of portfolios’ risk profile: Deterministic approach
8
Assessments of portfolios’ risk profile: Stochastic approach
9
Facing the annual payouts
10
Concluding remarks
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Concluding remarks
• Premiums tailored on the individual risk profile;
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Concluding remarks
• Premiums tailored on the individual risk profile; • Data scarcity =⇒ higher variance of lifetime distributions =⇒ higher variance of portfolio results;
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Concluding remarks
• Premiums tailored on the individual risk profile; • Data scarcity =⇒ higher variance of lifetime distributions =⇒ higher variance of portfolio results; • Impacts of life annuity portfolio extension:
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Concluding remarks
• Premiums tailored on the individual risk profile; • Data scarcity =⇒ higher variance of lifetime distributions =⇒ higher variance of portfolio results; • Impacts of life annuity portfolio extension: ◦ Higher variability; ◦ Higher premium income;
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Concluding remarks
• Premiums tailored on the individual risk profile; • Data scarcity =⇒ higher variance of lifetime distributions =⇒ higher variance of portfolio results; • Impacts of life annuity portfolio extension: ◦ Higher variability; ◦ Higher premium income; • What about the balance?
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Concluding remarks
• Premiums tailored on the individual risk profile; • Data scarcity =⇒ higher variance of lifetime distributions =⇒ higher variance of portfolio results; • Impacts of life annuity portfolio extension: ◦ Higher variability; ◦ Higher premium income; • What about the balance? • A number of numerical evaluations, according to a broad range of assumptions =⇒ sensitivity analysis;
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Concluding remarks
• Premiums tailored on the individual risk profile; • Data scarcity =⇒ higher variance of lifetime distributions =⇒ higher variance of portfolio results; • Impacts of life annuity portfolio extension: ◦ Higher variability; ◦ Higher premium income; • What about the balance? • A number of numerical evaluations, according to a broad range of assumptions =⇒ sensitivity analysis; • Numerical results witness the possibility of extending the life annuity business without worsening the portfolio risk profile.
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Thank you!
Thank you for your kind attention!
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