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475 Ch2 Insurance Pricing Part II.pptx

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475 Ch2 Insurance Pricing Part II.pptx

  1. 1. Company LOGO Life and Health Insurance Pricing Fundamentals Chapter 2 and 27~29 Part II
  2. 2. Ch2 Part 2 Agenda  Factors/information needed for life insurance pricing  Assumptions needed for pricing  Pricing examples 1. Renewable one-year term Life Insurance 2. Single premium whole life 3. Single premium immediate annuity
  3. 3. Factors/information Needed to Compute Life Insurance Premium Rates 1. Premium plan:  single premium, limited pay, or continuous pay.  Frequency 2. Death Benefit features 3. Age of the Insured 4. Gender of the Insured (not permitted in Montana) 5. Others, e.g., health condition, smoking/non- smoking, occupations, hobby Note: some factors are prohibited: e.g., race
  4. 4. Assumptions Needed to Compute Life Insurance Premium Rates Assumptions: the estimations about the future, may or may not actually come true. 1. Mortality rate  Mortality Table, usually gender-based (e.g., CSO, AMT, Select, Ultimate, valuation, smoker or nonsmoker, etc.) 2. Interest Rate 3. Expenses loading 4. Profit loading (to meet the target profit level)
  5. 5. Pricing principle  PV(E(net premium)) = PV(E(benefit))  PV(E(gross premium)) = PV(E(benefit))+PV(E(expense)) + PV(target profit)  Note:  PV: present value  E: expected
  6. 6. Pricing example 1: Renewal annual premium for renewable one year term 330/1.05=314.29 385/1.05=366.67 480/1.05=457.14 658/1.05=626.67 1000/1.05=952.38 Assume DB paid at the end of year. Net Renewal annual premium (Per $1000 DB) Assume guarantee interest rate is 5% 0.33*1000 =330
  7. 7. Pricing example 2: whole life single premium Whole life insurance, sold to a 95 year old. DB=$1000. Premium paid at the beginning of the year  Assume  Interest rate=5%  DB paid at the end of the year  What is the net single premium?
  8. 8. Pricing example 2: whole life single premium year x q(x) expected value of DB 1 95 0.32996 2 96 0.38455 3 97 0.4802 4 98 0.65789 5 99 1 Step 1: what is the expected value of the DB each year?
  9. 9. Pricing example 2: whole life single premium time 0 1 2 3 4 5 age 95 96 97 98 99 100 year x q(x) expected value of DB 1 95 0.32996 1000*q(95)=329.960 2 96 0.38455 1000*(1-q(95))*q(96)=257.664 3 97 0.4802 1000*(1-q(95))*(1-q(96))*q(97) =198.023 4 98 0.65789 1000*(1-q(95))*(1-q(96))*(1- q(97))*q(98) =141.021 5 99 1 1000*(1-q(95))*(1-q(96))*(1-q(97))*(1- q(98))*q(99) =73.332 Step 1: what is the expected value of the DB each year?
  10. 10. Pricing example 2: whole life single premium time 0 1 2 3 4 5 E(DB) 329.96 257.664 198.023 141.021 73.332 𝑃𝑉 𝐸(𝐷𝐵) = 329.96 1.05 + 257.664 1.052 + 198.023 1.053 + 141.021 1.054 + 73.332 1.055 =892.49 Step 3: Single premium=PV(E(DB)) =892.49 Step 2: what is present value of the expected DB?
  11. 11. Pricing example 3: Single Premium Immediate Pure Life Annuities  Find single net premium for a pure life annuity for a 96 year old, with $5,000 annual benefit  Assume  Interest rate = 10%  Annuity paid at the end of each year  Note: everyone dies by age 100 age Number of survivor 96 9831 97 6050 98 3145 99 1076 100 0
  12. 12. year Expected Payment=$5000 x prob. of surviving 1 2 3 4 Pricing example 3: Single Premium Immediate Pure Life Annuities Step 1: find out the expected annuity payment every year Time 0 1 2 3 4 Age 96 97 98 99 100
  13. 13. year Expected Payment=$5000 x prob. of surviving 1 5000*(6050/9831) =$3,077.001 2 5000*(3145/9831) =$1,599.532 3 5000*(1076/9831) =$547.25 4 5000*(0/9831)=0 Pricing example 3: Single Premium Immediate Pure Life Annuities Step 1: find out the expected annuity payment every year Time 0 1 2 3 4 Age 96 97 98 99 100
  14. 14. Pricing example 3: Single Premium Immediate Pure Life Annuities Step 2: find out the PV of the expected annuity payments Time 0 1 2 3 4 E(payment) $3077.001 $1599.532 $547.25 0 𝑃𝑉 𝐸(𝑝𝑎𝑦𝑚𝑒𝑛𝑡) = 3077.001 1.1 + 1599.532 1.12 + 547.25 1.13 + 0= $4,530.36 Step 3: Single premium=PV(E(annuity payment)) = $4,530.36
  15. 15. Gross premium  If the profit and expense loading is, such as 50% of the net premium, then  the gross premium=1.5*(net premium)

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