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September 2002 Arlington, Virginia

Intermediate Track II. September 2002 Arlington, Virginia. 1. Bornhuetter-Ferguson Method 2. Average Hindsight Method 3. Average Incremental Paid Method . This Session Will Discuss. BORNHUETTER- FERGUSON METHOD. Summary:

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September 2002 Arlington, Virginia

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  1. Intermediate Track II September 2002 Arlington, Virginia

  2. 1. Bornhuetter-Ferguson Method 2. Average Hindsight Method 3. Average Incremental Paid Method This Session Will Discuss

  3. BORNHUETTER- FERGUSON METHOD

  4. Summary: Project IBNR based on expected losses and the percentage of ultimate losses which are currently unreported. The Bornhuetter-Ferguson method is a combination of Expected Loss Ratio Method (loss ratio x premium) Paid or Incurred Loss Development Method (paid or incurred losses x loss development factor) Bornhuetter-Ferguson Method

  5. Steps to Project Ultimate Loss (1) Calculate Expected Losses (2) Calculate IBNR Factor (3) Calculate IBNR Reserve (4) Calculate estimated ultimate losses Bornhuetter-Ferguson Method

  6. Assumptions Earned Premium = $1,250 Incurred Losses = $600 Expected Loss Ratio = 65% CDF = 1.35 (derived from incurred loss development triangle) Bornhuetter-Ferguson Method

  7. Step 1 Calculate Expected Losses = Expected Loss Ratio x Earned Premium Earned Premium = $1,250 Expected Loss Ratio = 65% Expected Losses = $813 (1,250 x 0.65) [Expected losses may also be projected using (pure premium x exposure) OR (frequency x severity x exposure) ] Bornhuetter-Ferguson Method

  8. Step 2 Calculate IBNR Factor [IBNR Factor is the percent of ultimate losses still left to be reported] = IBNR / Ultimate Losses = Ultimate Loss - Incurred to Date Ultimate Loss = 1.000 - (Incurred to Date / Ultimate) = 1.000 - [1.000/(CDF)] CDF = 1.350 IBNR Factor = [1 - 1/1.350] = 26% Bornhuetter-Ferguson Method

  9. Step 3 Calculate IBNR Reserve = IBNR Factor x Expected Losses Expected Losses = $813 IBNR Factor = [1 - 1/1.350] = 26% IBNR Reserve = [$813 x 26%] = $211 Bornhuetter-Ferguson Method

  10. Step 4 Calculate Estimated Ultimate Losses = Incurred Losses + IBNR Reserve Incurred Losses = $600 IBNR Reserve = [$813 x 26%] = $211 Ultimate Losses = [$600 + $211] = $811 Bornhuetter-Ferguson Method

  11. Advantages Easy to use Compromises between loss development and expected loss ratio methods Avoid overreaction - doesn’t apply development factors to an unusual claim occurrence Suitable for new or volatile lines of business Can be used with no internal loss history Can also be used with paid data Bornhuetter-Ferguson Method

  12. Disadvantages Highly dependent on expected loss ratio or pure premium Requires development factors Bornhuetter-Ferguson Method

  13. Comparison of Methods Given: Earned Premium = $2,000 Expected Loss Ratio = 70 % Incurred Losses to Date = $750 Development Factor = 2.00 Bornhuetter-Ferguson Method

  14. 1) Expected Loss Ratio Method =Earned Premium x Expected Loss Ratio =$2,000 x 70% =$1,400 2) Loss Development Method =Incurred to Date x Development Factor =$750 x 2.00 =$1,500 3) Bornhuetter Ferguson Method = Incurred to Date + Expected Losses x (1-1/Dev. Factor) =$750 + $1,400 x [1 - 1/2.00] =$750 + $700 =$1,450 Bornhuetter-Ferguson Method

  15. Comparison of Methods: Illustration of Tempering Effect Given: One additional “large” claim of $150 Incurred Losses to Date = $900 Bornhuetter-Ferguson Method

  16. 1) Expected Loss Ratio Method =Earned Premium x Expected Loss Ratio =$2,000 x 70% =$1,400 2) Loss Development Method =Incurred to Date x Development Factor =$900 x 2.00 =$1,800 3) Bornhuetter Ferguson Method = Incurred to Date + Expected Losses x (1-1/Dev. Factor) =$900 + $1,400 x [1 - 1/2.00] =$900 + $700 =$1,600 Bornhuetter-Ferguson Method

  17. AVERAGE HINDSIGHT METHOD

  18. Summary: Estimate the expected ultimate losses for recent accident years based on “hindsight” average paid values per claim for more mature accident years. Average Hindsight Method

  19. Data Needed Cumulative Paid Loss Triangle Cumulative Closed (Paid) Claim Count Triangle Average Hindsight Method

  20. Steps to project Accident Year 1999 Ultimate Loss (1) Project ultimate losses for the four prior AY’s using paid loss development method (2) Project ultimate claim counts for all AY’s using claim count development (3) Calculate projected payment per claim from 36 months to ultimate (4) Calculate total future payments for AY 1999 (5) Calculate estimated ultimate losses for AY 1999 Average Hindsight Method

  21. Accident Year 1999 - Step 1 Project ultimate losses for the four prior AY’s using paid loss development method Average Hindsight Method

  22. Average Hindsight Method

  23. Average Hindsight Method

  24. Average Hindsight Method

  25. Accident Year 1999 - Step 2 Project ultimate claim counts for all AY’s using claim count development Average Hindsight Method

  26. Average Hindsight Method

  27. Average Hindsight Method

  28. Average Hindsight Method

  29. Accident Year 1999 - Step 3 Calculate projected payment per claim from 36 months to ultimate Average Hindsight Method

  30. Average Hindsight Method

  31. Accident Year 1999 - Steps 4 & 5 Calculate total future payments for AY 1999 Calculate estimated ultimate losses for AY 1999 Average Hindsight Method

  32. Average Hindsight Method

  33. Steps to Project Accident Year 2000 Ultimate Loss (1) Calculate projected payment per claim from 24 mos. to ultimate (using results from AY 1999 projection) (2) Calculate total future payments for AY 2000 (3) Calculate estimated ultimate losses for AY 2000 Average Hindsight Method

  34. Accident Year 2000 - Step 1 Calculate projected payment per claim from 24 mos. to ultimate (using results from AY 1999 projection) Average Hindsight Method

  35. Average Hindsight Method

  36. Accident Year 2000 - Steps 2 & 3 Calculate total future payments for AY 2000 Calculate estimated ultimate losses for AY 2000 Average Hindsight Method

  37. Average Hindsight Method

  38. Steps to Project Accident Year 2001 Ultimate Loss (1) Calculate projected payment per claim from 12 mos. to ultimate (using results from AY’s 1999 & 2000 projections) (2) Calculate total future payments for AY 2001 (3) Calculate estimated ultimate losses for AY 2001 Average Hindsight Method

  39. Accident Year 2001 - Step 1 (1) Calculate projected payment per claim from 12 mos. to ultimate (using results from AY’s 1999 & 2000 projections) Average Hindsight Method

  40. Average Hindsight Method

  41. Accident Year 2001 - Steps 2 & 3 Calculate total future payments for AY 2001 Calculate estimated ultimate losses for AY 2001 Average Hindsight Method

  42. Average Hindsight Method

  43. Advantages Relatively unaffected by changes in case reserving practices Can easily adjust trend assumptions Allows separate analysis of frequency and severity Disadvantages Sensitive to payment pattern shifts Averages highly variable when only a few claims May be insufficient if business has significantly changed (i.e. retentions dramatically increase) Too “formula-driven” Average Hindsight Method

  44. AVERAGE INCREMENTAL PAID METHOD

  45. Summary: Estimate the expected ultimate losses for recent accident years based on average incremental paid values per claim. Average Incremental Paid Method

  46. Data Needed: Ultimate Claim Counts Incremental Paid Loss Triangle Average Incremental Paid Method

  47. Average Incremental Paid Method Ultimate claim counts derived in average hindsight method - Slide 28

  48. Average Incremental Paid Method 12-24 column = Slide 24, column 3 (24 mos) - column 2 (12 mos)

  49. Steps to Project Ultimate Loss (1) Create triangle of incremental paid losses per ultimate claim (2) Calculate incremental payment trend factors and select projected trend factor (3) Calculate on-level incremental payments (4) Project future payment amounts (5) Calculate estimated ultimate losses Average Incremental Paid Method

  50. Step 1 Create triangle of incremental paid losses per ultimate claim Average Incremental Paid Method

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