eCompaniesInsuranceandPensionPlansChapter 3RiskManagementandFinanciallnstitutions3e,Chapter3,CopyrightJohnC.Hull2012
Insurance Companies and Pension Plans Chapter 3 Risk Management and Financial Institutions 3e, Chapter 3, Copyright © John C. Hull 2012 1
Types of Life Insurance (pages 41-45)Term lifeWhole lifeVariable lifeUniversal lifeEndowment lifeGroup life2RiskManagementandFinancialInstitutions3e,Chapter3,CopyrightJohnC.Hull2012
Types of Life Insurance (pages 41-45) ⚫ Term life ⚫ Whole life ⚫ Variable life ⚫ Universal life ⚫ Endowment life ⚫ Group life Risk Management and Financial Institutions 3e, Chapter 3, Copyright © John C. Hull 2012 2
Costof WholeLifeInsuranceCompared with Annual Premium(Figure3.1)7000060000Costperyear50000400003000020000AnnualPremiumSurplus1000004555657075804050603RiskManagementandFinanciallnstitutions3e,Chapter3CopyrightJohnC.Hull2012
Cost of Whole Life Insurance Compared with Annual Premium (Figure 3.1) Risk Management and Financial Institutions 3e, Chapter 3, Copyright © John C. Hull 2012 3 0 10000 20000 30000 40000 50000 60000 70000 40 45 50 55 60 65 70 75 80 Cost per year Surplus Annual Premium
Investment of Surplus Some contracts allow the policyholder tochoose how the surplus is investedThere are tax deferral advantagescompared with a regular investmentbecause no tax is paid until there is apayout on the policyRiskManagementandFinancialInstitutions3e,Chapter3,CopyrightJohnC.Hull20124
Investment of Surplus ⚫ Some contracts allow the policyholder to choose how the surplus is invested ⚫ There are tax deferral advantages compared with a regular investment because no tax is paid until there is a payout on the policy Risk Management and Financial Institutions 3e, Chapter 3, Copyright © John C. Hull 2012 4
Annuity Contracts (pages 45-46)Typicallyalumpsumpaymentisusedtobuyalife-time annuityAnnuity can be fixed or variableAnnuity can start immediately or be deferred Accumulated value can depend in a complicatedway on the performance of stock indicesThere may be penalty-free withdrawals5RiskManagementandFinancialInstitutions3e,Chapter3,CopyrightJohnC.Hull2012
Annuity Contracts (pages 45-46) ⚫ Typically a lump sum payment is used to buy a life-time annuity ⚫ Annuity can be fixed or variable ⚫ Annuity can start immediately or be deferred ⚫ Accumulated value can depend in a complicated way on the performance of stock indices ⚫ There may be penalty-free withdrawals Risk Management and Financial Institutions 3e, Chapter 3, Copyright © John C. Hull 2012 5
ExtractfromUSMortalityTables(2007): MaleAgeProb. death withinProb.SurvivalLifeexpectancy(yrs)oneyear3047.130.0014280.97147310.0014530.9700946.20320.0014870.9686845.273344.330.0015290.967246RiskManagementandFinancialInstitutions3e,Chapter3,CopyrightJohnC.Hull2012
Extract from US Mortality Tables (2007): Male Risk Management and Financial Institutions 3e, Chapter 3, Copyright © John C. Hull 2012 6 Age Prob. death within one year Prob. Survival Life expectancy (yrs) 30 0.001428 0.97147 47.13 31 0.001453 0.97009 46.20 32 0.001487 0.96868 45.27 33 0.001529 0.96724 44.33
ExtractfromUSMortalityTables(2007):FemaleAgeProb. death withinProb.SurvivalLifeexpectancy(yrs)oneyear3051.500.0006420.98466310.0006780.9840350.53320.0007210.9833649.56330.0007710.9826648.607RiskManagementandFinancialInstitutions3e,Chapter3,CopyrightJohnC.Hull2012
Extract from US Mortality Tables (2007): Female Risk Management and Financial Institutions 3e, Chapter 3, Copyright © John C. Hull 2012 7 Age Prob. death within one year Prob. Survival Life expectancy (yrs) 30 0.000642 0.98466 51.50 31 0.000678 0.98403 50.53 32 0.000721 0.98336 49.56 33 0.000771 0.98266 48.60
HowTables AreUsed InPricingLifeInsuranceConsider a female aged 30Probability of death during first year is 0.000642 Probability of death during second year is(1-0.000642)×0.000678Probability of death during third year is(1-0.000642)× (1-0.000678)×0.000721etcMinimum premium is such that present value of inflowsequals present value of outflows.8RiskManagementandFinancialInstitutions3e,Chapter3,CopyrightJohnC.Hull2012
How Tables Are Used In Pricing Life Insurance ⚫ Consider a female aged 30 ⚫ Probability of death during first year is 0.000642 ⚫ Probability of death during second year is (1-0.000642) × 0.000678 ⚫ Probability of death during third year is (1-0.000642) × (1-0.000678) ×0.000721 ⚫ etc ⚫ Minimum premium is such that present value of inflows equals present value of outflows. Risk Management and Financial Institutions 3e, Chapter 3, Copyright © John C. Hull 2012 8
Longevity Derivatives (page 50-51) Used by life insurance companies andpensionfunds A population is defined and coupon on abond depends on the number of membersof the population still alive9RiskManagementandFinancialInstitutions3e,Chapter3,CopyrightJohnC.Hull2012
Longevity Derivatives (page 50-51) ⚫ Used by life insurance companies and pension funds ⚫ A population is defined and coupon on a bond depends on the number of members of the population still alive Risk Management and Financial Institutions 3e, Chapter 3, Copyright © John C. Hull 2012 9
Property-Casualty Insurance Property insurance is concerned with lossor damage to property from fire, theft, etcCasualty insurance is concerned legalliability exposuresWhat are the biggest risks facing property-casualtyinsurers?10RiskManagementandFinancialInstitutions3e,Chapter3,CopyrightJohnC.Hull2012
Property-Casualty Insurance ⚫ Property insurance is concerned with loss or damage to property from fire, theft, etc ⚫ Casualty insurance is concerned legal liability exposures ⚫ What are the biggest risks facing propertycasualty insurers? Risk Management and Financial Institutions 3e, Chapter 3, Copyright © John C. Hull 2012 10