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8/2/2019 1C - Life Insurance Pricing 101
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Life Insurance Pricing 101Life Insurance Pricing 101
Actuaries Club of Hartford & Springfield
June 3, 2009
Scott D. Houghton, FSA, MAAA
Consulting Actuary
Valani Consulting
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PricingPricingWhat needs are met by life products?What needs are met by life products?
Life insurance death benefit protection
Longevity / income protection
Loss protection Tax planning
Retirement savings
Professional money management
Diversification
Risk management / guaranteed return
2
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Product Design ExamplesProduct Design ExamplesHow do products meet needs?How do products meet needs?
Term life insurance
Long term care insurance
Whole life insurance
Deferred annuity
Immediate annuity
3
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Product DesignProduct Design
ConsiderationsConsiderations
Marketing Distribution
Compensation Cost Structure
4
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Product DesignProduct Design
Cost structureCost structure
Premiums Single
Level
Prefunding? Increasing
Flexible
Spreads Insurance charges
Fees5
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Product DesignProduct Design
More ConsiderationsMore Considerations
Duration Term
Permanent
Benefits
Policy benefits Nonforfeiture benefits
Participation
Underwriting / risk selection6
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Product Design / Risk TransferProduct Design / Risk Transfer
What risks are transferred to theinsurer?
What risks can the insurerdiversify?
What risks need to be retainedand appropriately charged for?
7
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Risks in Insurance ProductsRisks in Insurance Products
Mortality
Longevity
Morbidity Persistency
Premium Persistency
Withdrawals
Disintermediation
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Risks in Insurance Products (2)Risks in Insurance Products (2)
Underwriting
Medical
Financial Pricing
Regulatory / Legal Risk
Expense risk
9
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Investment risks assumed byInvestment risks assumed by
insurersinsurers
Credit risk
Interest rate risk
Equity risk Liquidity risk
Call / prepayment risk
Reinvestment risk
Volatility
10
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Key goal of pricing life insuranceKey goal of pricing life insurance
productsproducts
Identify risks and charge
appropriately
11
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Pricing TechniquePricing Technique
Create product designIdentify risks
Make projection that capturesrisks, charges, and expenses
Use projection as tool todetermine charges
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Pricing ProjectionPricing Projection Contingent insured event assumptions
Financial markets, interest earnings assumptions
Benefits - assumptions Policy benefits
Nonforfeiture benefits
Expenses - assumptions
Profits
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Sources of Pricing AssumptionsSources of Pricing Assumptions
Company experience Industry experience, tables
15
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Pricing ExamplePricing Example
Annual Renewable TermAnnual Renewable Term
Not realistic products
Intended to illustrate process
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Pricing ExamplePricing Example
Annual Renewable TermAnnual Renewable Term
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
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Pricing ExamplePricing Example
Annual Renewable TermAnnual Renewable Term
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
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Pricing ExamplePricing Example
Annual Renewable TermAnnual Renewable Term
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 premiums19
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Annual Renewable TermAnnual Renewable Term
year qx tpx q Interest Face Benefits Net Prem tpx
l
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
Prem
paid Ben Paid Comm Exp CashFlow IRR
1 20.09% 687.05 595.00 206.12 250.00364.06 12.01%
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 24.21 147.8020
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Sensitivity TestingSensitivity Testing
Way to address uncertain assumption
ART Example - mortality
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ARTARTSensitivity Test 103% qSensitivity Test 103% qxx
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
Prem
paid Ben Paid Comm Expense CashFlow IRR
1 20.09% 687.05 612.85 206.12 250.00381.91
3.85%
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 22
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Stochastic TestingStochastic Testing
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 of10,000
23
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Stochastic TestingStochastic Testing
Claims Occurances
2 13 1
4 4
5 32
6 54
7 89
8 144
9 176
10 227
11 231
12 24113 198
Claims Occurances
14 166
15 127
16 103
17 76
18 48
19 30
20 25
21 1122 8
23 4
24 325 1
24
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Stochastic TestingStochastic Testing
0
50
100
150
200
250
300
1 3 5 7 9 11 13 15 17 19 21 23 25
Occurances
Occurances
25
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Accounting, liabilities, andAccounting, liabilities, and
capitalcapital
Prefunding creates liability
Different ways to measure and calculate
US Statutory
Principles Based Approaches
US GAAP
IFRS Economic
Capital requirements
Risk Based Capital, PBA
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Capital RequirementsCapital Requirements
Capital requirements
Risk Based Capital,
PBA
27
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Common Profit MeasuresCommon Profit Measures
IRR of Distributable Earnings
Present Value of Profits
IRR of GAAP Equity
Present Value of Profits/Present Value of
Fund Value added / economic
Market consistent28
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Annual Renewable Term (again!)Annual Renewable Term (again!)
year qx tpx q Interest Face Benefits Net Prem tpx
l
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
Prem
paid Ben Paid Comm Expense CashFlow IRR
1 20.09% 687.05 595.00 206.12 250.00364.06 12.01%
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 24.21 147.8029
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Annual Renewable Term 115% qAnnual Renewable Term 115% qxx
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 1159.91 970.000.9500
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
453.312 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 25.5564.47
5 20.09% 1654.28 1645.28 49.63 24.18 64.8130
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Pricing ExamplePricing Example
10 Year Level Term10 Year Level Term
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
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Pricing ExamplePricing Example
10 Year Level Term10 Year Level Term
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 $500,00032
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Pricing ExamplePricing Example
10 Year Level Term10 Year Level Term
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 premiums33
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10 Year Level Term10 Year Level Term
34
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
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10 Year Level Term10 Year Level Term
35
year PremGr CommGr Exp G BenefitsG ReservesG
1 2280.00 684.0000 250.0000 595.00 1121.40
2 2280.00 68.4000 30.0000 1010.00 1979.89
3 2280.00 68.4000 30.0000 1365.00 2534.88
4 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
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10 Year Level Term10 Year Level Term
36
year Benefits n Premiumn Reservesn Comm n Expensen
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 25.575 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
0
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10 Year Level Term10 Year Level Term
37
11.99%
year Assets Inv Inc
PreTax
Profit Taxes
After
Tax
Profit Capital
Dist
Earn
1 751.00 30.04340.36
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
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Pricing ExamplePricing Example
Deferred AnnuityDeferred Annuity
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
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Pricing ExamplePricing Example
Deferred AnnuityDeferred Annuity
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 bonds39
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Pricing ExamplePricing Example
Deferred AnnuityDeferred Annuity
These assumptions result in profit / IRR of 12%after tax distributable under level scenario
Embedded derivative Interest rate risk
Stochastic results
Lognormal interest rate model
Real world generator
Historical volatility
10,000 Scenarios
40
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When to use StochasticWhen to use Stochastic
AnalysisAnalysis
Tool to see whole picture or at least more of thepicture
Embedded derivatives Risk Neutral analysis
Real World analysis
Decision tool for company practices Non-diversifiable risk analysis
41
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Stochastic ResultsStochastic Results -- AnnuityAnnuity
0
500
1000
1500
2000
2500
55 50 45 40 35 30 25 20 15 10 5 0 5 10 15 20 25 30
Occurances
42
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New Product FeaturesNew Product Features
Return of premium term insurance
Combination annuity products
Lifetime annuities
43
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Methods of risk transferMethods of risk transfer
Reinsurance
Mortality risk
Financial risks
Reflect in pricing
Securitization Hedging
44
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SecuritizationSecuritization
45
Insurer
Captive
Reinsurer
Security
Issuer
Investors
Bank
premium
claims
Return
proceeds
pr
oc
eeds
Guar-
anteefee
re
tu
rn
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Impact of Principle BasedImpact of Principle Based
Approaches on PricingApproaches on Pricing
Assets and investments tied to liability side More need to specify investments when pricing
More economic, less opportunity forsecuritization
Management of investment risks
Reserves prospective, capital isnt Current products will need to support PBA capital
46
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End of Life InsuranceEnd of Life Insurance
Pricing 101Pricing 101
Actuaries Club of Hartford & Springfield
June 3, 2009
Scott D. Houghton, FSA, MAAA
Consulting Actuary
Valani Consulting