Stat 476 Life Contingencies II. Participating and Universal Life Insurance

Transcription

1 Stat 476 Life Contingencies II Participating and Universal Life Insurance

2 Purposes of Different Types of Insurance Term Insurance Solely indemnification No investment income or surrender benefits Whole Life Insurance Some payment is inevitable, either due to surrender or death. There is some investment or tax benefit in addition to indemnification. 2

3 Risks in Whole Life Insurance A whole life policy is issued to someone younger may have an expected benefit 40+ years in the future. To account for the fact that there are no fixed-income assets that many years in the future, the insurer may include an interest spread when pricing the policy. If the spread is too small, the insurer will be overly exposed to interest rate risk. If the spread is too large, the product will be too expensive and unattractive to potential customers. 3

4 Participating Insurance One option is to make the benefits and/or premiums more flexible. This is the justification for participating (or par) insurance, also called with-profit outside of North America. Starts with level, conservative premiums A portion of any surplus is returned to the policyholders in many ways Cash Premium reduction Increasing the sum insured Purchasing other benefits, e.g. term insurance They are not as popular now because they are not as flexible as Universal Life (which we will talk about soon) 4

5 Participating Insurance Example Annual $100,000 whole life participating contract on (60) who follows the SUSM Annual premium = $2300 Reserves are calculated using FPT (i = 0.05) Cash value = max ((t 4) + 10%, 90%) of year-end reserve plus the dividend due at the end of their last contract year. Surrender probability P s assumptions P s = 0.05 for 1 t 9 P s = for 10 t 29 P s = 1 for t = 30 90% of surplus in each year after the first is distributed as a cash dividend. Acquisition expenses = $1800 Premium expenses = $100 Investment interest = 6%, discount rate = 10% 5

6 Notes on Profit Distribution Cash is attractive, easy to understand and offers flexibility Cash may be taxable If they prefer extra death benefits, they could buy the insurance, but it may have acquisition costs Limited participation for surrendered policies may lead to loss of trust and dissatisfaction Cash requires the insurer to liquidate assets, reducing smoothness and forcing more cautious investing Cash can be expensive to disperse 6

7 Universal Life (UL) Insurance UL policies are very popular in the United States. Premiums are deposited into a notional account. Insurer shares the profits through a credited interest rate. The account value is the balance of funds in the notional account (often surrender value, after initial period). Monthly deductions are taken from the notional account to cover the cost of insurance cover and expenses. 7

8 UL Design Features Death Benefit = Account Value + Additional Death Benefit (ADB) Corridor factor requirement: total DB/Account Value Type A: Level total death benefit Type B: Level ADB Premiums: subject to some minimum level and payment term, but are highly flexible Expenses, management expense rate (MER), expressed either as a percent of premiums and account value and/or a flat fee. Credited Interest: profit sharing Cost of Insurance (CoI): Cost of providing death cover Surrender Charge: Reduction in the account value to get the cash value, enables the insurer to pay acquisition expenses No-lapse guarantee: death benefit cover continues as long as some minimum premium is paid. 8

9 Projecting Account Values Notation AV t Account value at time t EC t Expense charge deducted at the beginning of year t CoI t Cost of insurance deducted at the beginning of year t i c t Credited interest rate during year t P t Premium paid at the start of year t DB t Death benefit cover in year t CV t Cash value paid on surrender at the end of year t Fundamental recursion equation (AV t 1 + P t EC t CoI t )(1 + it c ) = AV t 9

10 Universal Life Type B Example A UL policy is sold to a 45-year old man (following SSSM). Premiums are $2250 for 6 years, with no premiums due thereafter. CoI: 120% of mortality (SSSM) using i = 0.05 Expenses: $2000 acquisition, $45 + 1% of premium at the start of each year, $50 on surrender, $100 on death. ADB: $100,000 Interest credited with a spread of 2% Interest earned on insurer s funds at 7% Hurdle rate: 10% Surrenders occur at year end according to the following table t q 45+t t Penalty Full account value is held as reserve. 10

11 Universal Life Type A Because the total death benefit is a constant amount (denoted face amount, FA), the ADB is equal to the difference between the FA and the account value. This assumes that the corridor factor (γ) does not apply. The actual benefit will be and the ADB will be max [FA, γ t AV t ] max [FA AV t, (γ t 1)AV t ] 11

12 Universal Life Type A Example A UL policy is sold to a 45-year old man (following SSSM). Face Amount $100,000 Surrender rates and penalties and corridor factors are in the spreadsheet Premiums are $3500 for the entirety of the policy. CoI: 120% of mortality (SSSM) using i = 0.04 Account Value Expenses: $ % of premium acquisition, 3% of premium at the start of each year. Profit Test Expenses: 62% of premium acquisition, 2% of premium at the start of each renewal year, $50 on surrender, $100 on death. Interest credited with a spread of 2% Interest earned on insurer s funds at 6% Hurdle rate: 10% Full account value is held as reserve. 12