1c - life insurance pricing 101

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

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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

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Product DesignProduct Design

ConsiderationsConsiderations

Marketing Distribution

Compensation Cost Structure

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Cost structureCost structure

Premiums Single

Level

Prefunding? Increasing

Flexible

Spreads Insurance charges

Fees5


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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?

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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

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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

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Key goal of pricing life insuranceKey goal of pricing life insurance

productsproducts

Identify risks and charge

appropriately

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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

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Pricing ExamplePricing Example

Annual Renewable TermAnnual Renewable Term

Not realistic products

Intended to illustrate process

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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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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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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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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


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

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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

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0

50

100

150

200

250

300

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

Occurances

Occurances

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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

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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!)


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


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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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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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



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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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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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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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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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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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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

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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


Investment in 7 year corporate bonds39


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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

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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

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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

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New Product FeaturesNew Product Features

Return of premium term insurance

Combination annuity products

Lifetime annuities

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Methods of risk transferMethods of risk transfer

Reinsurance

Mortality risk

Financial risks

Reflect in pricing

Securitization Hedging

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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

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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

1c - life insurance pricing 101

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