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1C - Life Insurance Pricing 101

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Life Insurance Pricing 101
Actuaries’ Club of Hartford & Springfield
June 3, 2009
Scott D. Houghton, FSA, MAAA
Consulting Actuary
Valani Consulting

1

Pricing

What needs are met by life products?
y
y
y
y
y
y
y
y

Life insurance death benefit protection
Longevity / income protection
Loss protection
Tax planning
Retirement savings
Professional money management
Diversification
Risk management / guaranteed return
2

Product Design Examples
How do products meet needs?
y Term

life insurance
y Long term care insurance
y Whole life insurance
y Deferred annuity
y Immediate annuity

3

Product Design
Considerations
Marketing
y Distribution
y Compensation
y Cost Structure
y

4

Product Design
Cost structure
y Premiums
◦ Single
◦ Level
x Prefunding?

◦ Increasing
◦ Flexible

y Spreads
y Insurance

charges

y Fees
5

Product Design
More Considerations
y Duration
◦ Term
◦ Permanent
y

Benefits
◦ Policy benefits
◦ Nonforfeiture benefits

Participation
y Underwriting / risk selection
y

6

Product Design / Risk Transfer
y What

risks are transferred to the
insurer?
y What risks can the insurer
diversify?
y What risks need to be retained
and appropriately charged for?
7

Risks in Insurance Products
y
y
y
y
y
y
y

Mortality
Longevity
Morbidity
Persistency
Premium Persistency
Withdrawals
Disintermediation
8

Risks in Insurance Products (2)
y

Underwriting
◦ Medical
◦ Financial

Pricing
y Regulatory / Legal Risk
y Expense risk
y

9

Investment risks assumed by
insurers
y
y
y
y
y
y
y

Credit risk
Interest rate risk
Equity risk
Liquidity risk
Call / prepayment risk
Reinvestment risk
Volatility
10

Key goal of pricing life insurance
products
y Identify

risks and charge
appropriately

11

Other goals of pricing
y Sufficient

rates / charges
y Equitable rates / charges
y Competitive rates / charges

12

Pricing Technique
y Create

product design
y Identify risks
y Make projection that captures
risks, charges, and expenses
y Use projection as tool to
determine charges
13

Pricing Projection
Contingent insured event – assumptions
y Financial markets, interest earnings –
assumptions
y Benefits - assumptions
y

◦ Policy benefits
◦ Nonforfeiture benefits

Expenses - assumptions
y Profits
y

14

Sources of Pricing Assumptions
y Company

experience
y Industry experience, tables

15

Pricing Example
Annual Renewable Term
y Not

realistic products
y Intended to illustrate process

16

Pricing Example
Annual Renewable Term
y
y
y
y
y
y

What needs are being met?
Design – current and guaranteed premiums
Renewable to age 60
Main risks – mortality and persistency
Marketing – company and independent agents
Paramedical underwriting

17

Pricing Example
Annual Renewable Term
y
y
y
y
y
y
y

Age 55 Example (M&F)
5% Lapses per year
Renewable to age 60
Mortality assumption 90-95 SOA Basic (S&U)
Profit goal: IRR of 12% (pretax)
Liabilities and capital not material – ignored assumption
Face amount $500,000
18

Pricing Example
Annual Renewable Term
y
y
y
y
y
y
y

Commissions 30% first year, 3% renewal
Other Issue Expenses $250
Maintenance Expenses $30 per year
Deaths at end of year (assumption)
Premiums at beginning of year (assumption)
4% interest (assumption)
Current premiums based on percentage load on
(pricing) net premiums
19

Annual Renewable Term
year

qx

tpx q

1 0.00119

1.000

4% 500,000

595.00

572.12 1.0000

2 0.00202

0.999

4% 500,000 1008.80

970.00 0.9500

3 0.00273

0.997

4% 500,000 1360.62

1308.29 0.9025

4 0.00316

0.994

4% 500,000 1570.63

1510.22 0.8574

5 0.00355

0.991

4% 500,000 1758.90

1691.25 0.8145

Load
1 20.09%

Interest

Prem
paid Ben Paid

Face Benefits Net Prem tpx‐ l

Comm

Exp CashFlow

687.05

595.00

206.12

250.00

2 20.09% 1106.63

958.36

33.20

28.47

86.60

3 20.09% 1417.94 1227.96

42.54

26.99

120.45

4 20.09% 1554.96 1346.62

46.65

25.57

136.12

5 20.09% 1654.28 1432.64

49.63

24.21

147.80

IRR

‐364.06 12.01%

20

Sensitivity Testing
y Way

to address uncertain assumption
y ART Example - mortality

21

ART – Sensitivity Test 103% qx
year

qx

tpx q Interest

Face Benefits Net Prem tpx‐ l

1 0.00123

1.000

4% 500,000 612.85

572.12 1.0000

2 0.00208

0.999

4% 500,000 1039.02

970.00 0.9500

3 0.00281

0.997

4% 500,000 1401.31 1308.29 0.9025

4 0.00325

0.994

4% 500,000 1617.46 1510.22 0.8574

5 0.00366

0.991

4% 500,000 1811.17 1691.25 0.8145

Load
1 20.09%

Prem
paid Ben Paid

Comm Expense CashFlow

687.05

612.85

206.12 250.00

2 20.09% 1106.63

987.07

33.20

28.47

57.89

3 20.09% 1417.94 1264.68

42.54

26.99

83.74

4 20.09% 1554.96 1386.77

46.65

25.56

95.97

5 20.09% 1654.28 1475.21

49.63

24.21

105.23

IRR

‐381.91 ‐3.85%

22

Stochastic Testing
y
y
y
y
y
y

Additional way to address uncertain assumption
ART Example - mortality
Assume I sell 10,000 policies of $500,000
First year qx is 0.00119
So 11.9 claims expected
Distribution can be simulated with groups of
10,000

23

Stochastic Testing
Claims

2
3
4
5
6
7
8
9
10
11
12
13

Occurances

1
1
4
32
54
89
144
176
227
231
241
198

Claims

14
15
16
17
18
19
20
21
22
23
24
25

Occurances

166
127
103
76
48
30
25
11
8
4
3
1

24

Stochastic Testing
Occurances
300
250
200
150

Occurances

100
50
0
1 3 5 7 9 11 13 15 17 19 21 23 25

25

Accounting, liabilities, and
capital
y
y

Prefunding – creates liability
Different ways to measure and calculate
y
y
y
y
y

y

US Statutory
Principles Based Approaches
US GAAP
IFRS
Economic

Capital requirements
y Risk Based Capital, PBA
26

Capital Requirements
y Capital

requirements

yRisk Based Capital,
yPBA

27

Common Profit Measures
IRR of Distributable Earnings
y Present Value of Profits
y IRR of GAAP Equity
y Present Value of Profits/Present Value of
Fund
y Value added / economic
y Market consistent
y

28

Annual Renewable Term (again!)
year

qx

tpx q

1 0.00119

1.000

4% 500,000

595.00

572.12 1.0000

2 0.00202

0.999

4% 500,000 1008.80

970.00 0.9500

3 0.00273

0.997

4% 500,000 1360.62 1308.29 0.9025

4 0.00316

0.994

4% 500,000 1570.63 1510.22 0.8574

5 0.00355

0.991

4% 500,000 1758.90 1691.25 0.8145

Load
1 20.09%

Interest

Prem
paid Ben Paid

Face Benefits Net Prem tpx‐ l

Comm Expense CashFlow

687.05

595.00

206.12

250.00

2 20.09% 1106.63

958.36

33.20

28.47

86.60

3 20.09% 1417.94 1227.96

42.54

26.99

120.45

4 20.09% 1554.96 1346.62

46.65

25.57

136.12

5 20.09% 1654.28 1432.64

49.63

24.21

147.80

IRR

‐364.06 12.01%

29

Annual Renewable Term 115% qx
year

qx

tpx q

Interest

Face Benefits Net Prem tpx‐ l

1 0.00137

1.000

4%

500,000 684.25

572.12 1.0000

2 0.00232

0.999

4%

500,000 1159.91

970.00 0.9500

3 0.00314

0.996

4%

500,000 1563.96 1308.29 0.9025

4 0.00363

0.993

4%

500,000 1804.61 1510.22 0.8574

5 0.00408

0.990

4%

500,000 2019.97 1691.25 0.8145

Load Prem paid

Ben Paid

Comm

Exp CashFlow IRR

1

20.09%

687.05

684.25

206.12 250.00 ‐453.31

2

20.09%

1106.63

1101.91

33.20

28.46

‐56.95

3

20.09%

1417.94

1411.47

42.54

26.98

‐63.05

4

20.09%

1554.96

1547.23

46.65

25.55

‐64.47

5

20.09%

1654.28

1645.28

49.63

24.18

‐64.81
30

Pricing Example
10 Year Level Term
y
y
y
y
y
y
y

Design – 10 year guaranteed premiums
Main risks – mortality, persistency
Some investment risk
Some prefunding
Marketing – company and independent agents
Paramedical underwriting
10 year product – not renewable
31

Pricing Example
10 Year Level Term
y
y
y
y
y
y
y

Age 55 Example (F)
5% Lapses per year
Mortality assumption 90-95 SOA Basic (S&U)
Profit goal: IRR of 12% after tax distributable
Liabilities – NAIC Valuation of Life Insurance
Policies Model Regulation
Capital 4% of premium, 0.30% of face amount
Face amount $500,000
32

Pricing Example
10 Year Level Term
y
y
y
y
y
y
y

Commissions 30% first year, 3% renewal
Other Issue Expenses $250
Maintenance Expenses $30 per year
Deaths at end of year (assumption)
Premiums at beginning of year (assumption)
4% interest (assumption)
Current premiums based on percentage load on
(pricing) net premiums
33

10 Year Level Term
year

qx

tpx q

Interest

Face

tpx‐ l

1

0.00119

1.000

4%

500,000

1.0000

2

0.00202

0.999

4%

500,000

0.9500

3

0.00273

0.997

4%

500,000

0.9025

4

0.00316

0.994

4%

500,000

0.8574

5

0.00355

0.991

4%

500,000

0.8145

6

0.00395

0.987

4%

500,000

0.7738

7

0.00447

0.984

4%

500,000

0.7351

8

0.00510

0.979

4%

500,000

0.6983

9

0.00578

0.974

4%

500,000

0.6634

10

0.00646

0.968

4%

500,000

0.6302
34

10 Year Level Term
year

Prem‐Gr

Comm‐Gr

Exp ‐ G Benefits‐G Reserves‐G

1

2280.00

684.0000 250.0000

2

2280.00

68.4000

3

2280.00

4

595.00

1121.40

30.0000

1010.00

1979.89

68.4000

30.0000

1365.00

2534.88

2280.00

68.4000

30.0000

1580.00

2908.17

5

2280.00

68.4000

30.0000

1775.00

3108.86

6

2280.00

68.4000

30.0000

1975.00

3121.60

7

2280.00

68.4000

30.0000

2235.00

2875.09

8

2280.00

68.4000

30.0000

2550.00

2298.80

9

2280.00

68.4000

30.0000

2890.00

1347.92

10

2280.00

68.4000

30.0000

3230.00

0.00
35

10 Year Level Term
year Benefits ‐n Premium‐n Reserves‐n Comm ‐ n Expense‐n
1

595.00

2280.00

1121.40

684.00

250.00

2

958.36

2163.42

1878.65

64.90

28.47

3

1227.96

2051.10

2280.39

61.53

26.99

4

1346.62

1943.23

2478.61

58.30

25.57

5

1432.64

1840.23

2509.22

55.21

24.21

6

1508.98

1742.01

2385.03

52.26

22.92

7

1615.84

1648.38

2078.61

49.45

21.69

8

1743.57

1558.96

1571.81

46.77

20.51

9

1867.67

1473.46

871.10

44.20

19.39

10

1971.56

1391.69

0.00

41.75

18.31
36

10 Year Level Term
PreTax
Profit

Taxes

After
Tax
Profit Capital

11.99%

Dist
Earn

year

Assets

Inv Inc

1

751.00

30.04

‐340.36 ‐119.13 ‐221.24 1591.20‐1812.44

2

1862.70

74.51

428.95 150.13 278.82 1509.84 360.18

3

2597.31

103.89

436.77 152.87 283.90 1431.45 362.29

4

3110.05

124.40

438.92 153.62 285.30 1356.17 360.58

5

3438.23

137.53

435.09 152.28 282.81 1284.29 354.69

6

3596.08

143.84

425.89 149.06 276.83 1215.74 345.37

7

3557.47

142.30

410.11 143.54 266.57 1150.39 331.92

8

3305.58

132.22

387.13 135.50 251.63 1087.99 314.04

9

2847.77

113.91

356.81 124.89 231.93 1028.32 291.60

10

2207.84

88.31

319.48 111.82 207.66 971.25 264.72
37

Pricing Example
Deferred Annuity
y
y
y
y
y
y
y
y
y

Single Premium Deferred Annuity
Commissions 6% first year
Issue Expenses $90
Maintenance Expenses $30 per year
1.50% spread, portfolio crediting
Investment in 7 year corporate bonds
3% minimum credited rate
7% declining surrender charge
$50,000 average size

38

Pricing Example
Deferred Annuity
y
y
y
y
y
y
y
y

Age 55 Example (M)
5% Lapses per year, 30% shock; interest sensitive
Mortality assumption 70% table 1983 A
Profit goal: IRR of 12% after tax distributable
Liabilities – CARVM
Capital 3% of reserves
Face amount $500,000
Investment in 7 year corporate bonds
39

Pricing Example
Deferred Annuity
y
y
y
y

These assumptions result in profit / IRR of 12%
after tax distributable under level scenario
Embedded derivative
Interest rate risk
Stochastic results
y
y
y
y

Lognormal interest rate model
Real world generator
Historical volatility
10,000 Scenarios
40

When to use Stochastic
Analysis
y
y

Tool to see whole picture or at least more of the
picture
Embedded derivatives
y Risk Neutral analysis
y Real World analysis

y
y

Decision tool for company practices
Non-diversifiable risk analysis

41

Stochastic Results - Annuity
Occurances
2500
2000
1500
1000
500
0
‐55 ‐50 ‐45 ‐40 ‐35 ‐30 ‐25 ‐20 ‐15 ‐10 ‐5 0

5 10 15 20 25 30

42

New Product Features
y
y
y

Return of premium term insurance
Combination annuity products
Lifetime annuities

43

Methods of risk transfer
y Reinsurance

y Mortality risk
y Financial risks
y Reflect in pricing
y Securitization
y Hedging
44

Bank

Securitization
premium
Insurer

claims

Guarantee

fee

Captive
Reinsurer

Return

Security
Issuer

proceeds

re
tu
rn

pr
oc
ee
ds

Investors
45

Impact of Principle Based
Approaches on Pricing
y

Assets and investments tied to liability side
y More need to specify investments when pricing

y
y
y

More economic, less opportunity for
securitization
Management of investment risks
Reserves prospective, capital isn’t
y Current products will need to support PBA capital

46

End of Life Insurance
Pricing 101
Actuaries’ Club of Hartford & Springfield
June 3, 2009
Scott D. Houghton, FSA, MAAA
Consulting Actuary
Valani Consulting

47

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