Presentation of the Paper 02-2020 of the MIB DemoLab - The special-rate life annuities

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

November 19, 2020

2 / 32

Introduction and motivation

• "Weak" features of traditional life annuity product (SPIA);

November 19, 2020

3 / 32

Introduction and motivation

• "Weak" features of traditional life annuity product (SPIA); • How to design more attractive products (from customer perspective);

November 19, 2020

3 / 32

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.

November 19, 2020

3 / 32

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

4 / 32

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

5 / 32

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

6 / 32

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

7 / 32

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

November 19, 2020

8 / 32

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

9 / 32

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

November 19, 2020

10 / 32

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

November 19, 2020

11 / 32

Market issues

(cont’d)

Statistical data (2) Figure 10: Age-distribution of deaths for males age 60

November 19, 2020

12 / 32

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

November 19, 2020

13 / 32

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

14 / 32

Biometric model

Figure 12: Curves of deaths for different life annuity sub-portfolios

Standard life annuities Enhanced life annuities Impaired life annuities

Age

November 19, 2020

15 / 32

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

16 / 32

The actuarial model

• Portfolio structures:

November 19, 2020

17 / 32

The actuarial model

• Portfolio structures: ◌ subportfolio SP1 initially consisting of n1 standard life annuities;

November 19, 2020

17 / 32

The actuarial model

• Portfolio structures: ◦ subportfolio SP1 initially consisting of n1 standard life annuities; ◦ subportfolio SP2 initially consisting of n2 enhanced life annuities;

November 19, 2020

17 / 32

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.

November 19, 2020

17 / 32

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:

November 19, 2020

17 / 32

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;

November 19, 2020

17 / 32

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;

November 19, 2020

17 / 32

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;

November 19, 2020

17 / 32

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.

November 19, 2020

17 / 32

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

18 / 32

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

November 19, 2020

19 / 32

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

20 / 32

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

21 / 32

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

November 19, 2020

22 / 32

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

23 / 32

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

November 19, 2020

24 / 32

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

November 19, 2020

25 / 32

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

November 19, 2020

26 / 32

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

November 19, 2020

27 / 32

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

28 / 32

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

November 19, 2020

29 / 32

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

30 / 32

Concluding remarks

• Premiums tailored on the individual risk profile;

November 19, 2020

31 / 32

Concluding remarks

• Premiums tailored on the individual risk profile; • Data scarcity =⇒ higher variance of lifetime distributions =⇒ higher variance of portfolio results;

November 19, 2020

31 / 32

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:

November 19, 2020

31 / 32

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;

November 19, 2020

31 / 32

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?

November 19, 2020

31 / 32

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;

November 19, 2020

31 / 32

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.

November 19, 2020

31 / 32

Thank you!

Thank you for your kind attention!

November 19, 2020

32 / 32