Intermediate Track II
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1 Intermediate Track II September 2000 Minneapolis, Minnesota 1
2 This Session Will Discuss 1. Bornhuetter-Ferguson Method 2. Average Hindsight Method 3. Average Incremental Paid Method 2
3 BORNHUETTER- FERGUSON METHOD 3
4 Bornhuetter-Ferguson Method 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) 4
5 Bornhuetter-Ferguson Method Steps to Project Ultimate Loss (1) Calculate Expected Losses (2) Calculate IBNR Factor (3) Calculate IBNR Reserve (4) Calculate estimated ultimate losses. 5
6 Bornhuetter-Ferguson Method Assumptions Earned Premium = $1,250 Incurred Losses = $600 Expected Loss Ratio = 65% CDF = 1.35 (derived from incurred loss development triangle) 6
7 Bornhuetter-Ferguson Method 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) ] 7
8 Bornhuetter-Ferguson Method 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 = (Incurred to Date / Ultimate) = [1.000/(CDF)] CDF = IBNR Factor = [1-1/1.350] = 26% 8
9 Bornhuetter-Ferguson Method 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 9
10 Bornhuetter-Ferguson Method Step 4 Calculate Estimated Ultimate Losses = Incurred Losses + IBNR Reserve Incurred Losses = $600 IBNR Reserve = [$813 x 26%] = $211 Ultimate Losses = [$600 + $211] = $811 10
11 Bornhuetter-Ferguson Method 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 11
12 Bornhuetter-Ferguson Method Disadvantages Highly dependent on expected loss ratio or pure premium Requires development factors 12
13 Bornhuetter-Ferguson Method Comparison of Methods Given: Earned Premium = $2,000 Expected Loss Ratio = 70 % Incurred Losses to Date = $750 Development Factor =
14 Bornhuetter-Ferguson Method 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 14
15 Bornhuetter-Ferguson Method Comparison of Methods: Illustration of Tempering Effect Given: One additional large claim of $150 Incurred Losses to Date = $900 15
16 Bornhuetter-Ferguson Method 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 16
17 AVERAGE HINDSIGHT METHOD 17
18 Average Hindsight Method Summary: Estimate the expected ultimate losses for recent accident years based on hindsight average paid values per claim for more mature accident years. 18
19 Average Hindsight Method Data Needed Cumulative Paid Loss Triangle Cumulative Closed (Paid) Claim Count Triangle 19
20 Average Hindsight Method Steps to project Accident Year 1997 Ultimate Loss (1) Project ultimate losses for 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 1997 (5) Calculate estimated ultimate losses for AY
21 Average Hindsight Method Accident Year Step 1 Project ultimate losses for AY s using paid loss development method 21
22 Average Hindsight Method XYZ Auto Insurance Company Cumulative Paid Losses ($000) Accident Months of Development Year $50.0 $80.0 $98.2 $107.8 $113.2 $117.2 $
23 Average Hindsight Method XYZ Auto Insurance Company Development of Paid Losses Months of Development Acc Year Ult year avg Selected CDF Diagonal Ultimate
24 Average Hindsight Method XYZ Auto Insurance Company Cumulative Paid Losses ($000) Accident Months of Development Year Ultimate 1993 $50.0 $80.0 $98.2 $107.8 $113.2 $117.2 $119.7 $ * * * Ultimate losses from Slide 23 24
25 Average Hindsight Method Accident Year Step 2 Project ultimate claim counts for all AY s using claim count development 25
26 Average Hindsight Method XYZ Auto Insurance Company Cumulative Number of Closed Claims Accident Months of Development Year
27 Average Hindsight Method XYZ Auto Insurance Company Development of Closed Claims Months of Development Acc Year Ult year avg Selected CDF Diagonal Ultimate
28 Average Hindsight Method XYZ Auto Insurance Company Cumulative Number of Closed Claims Accident Months of Development Year Ultimate Ultimate claim counts from Slide 27 28
29 Average Hindsight Method Accident Year Step 3 Calculate projected payment per claim from 36 months to ultimate 29
30 Average Hindsight Method XYZ Auto Insurance Company Calculation of Future Payment per Claim - 36 Months to Ultimate Estimated Number of Number Estimated Paid Estimated Ultimate Closed to Settle Average Accident Ultimate Losses at Future Number Claims at Beyond Future Year Losses 36 Months Payments of Claims 36 Months 36 Mos Payment (1) (2)=Slide 24 (3)=Slide 24 (4)=(2)-(3) (5)=Slide 28 (6)=Slide 28 (7)=(5)-(6) (8)=(4)/(7) 1993 $119,700 $98,200 $21, $1, , ,500 25, , , ,000 33, , , ,200 38, ,345 Fitted forecasted value for AY 1997 $2,561 30
31 Average Hindsight Method Accident Year Steps 4 & 5 Calculate total future payments for AY 1997 Calculate estimated ultimate losses for AY
32 Average Hindsight Method XYZ Auto Insurance Company Estimated Ultimate Losses: Accident Year 1997 (1) Forecasted Average Future Payment [Slide 30] $2,561 (2) Number of Future Claims to Settle [Slide 28] (Ultimate - Closed Claims) = (3) Estimated Future Loss Payments [ (1) x (2) ] $49,693 (4) Paid Losses to Date [Slide 24] $226,400 (5) Estimated Ultimate Losses [ (3) + (4) ] $276,093 32
33 Average Hindsight Method Steps to Project Accident Year 1998 Ultimate Loss (1) Calculate projected payment per claim from 24 mos. to ultimate (using results from AY 1997 projection) (2) Calculate total future payments for AY 1998 (3) Calculate estimated ultimate losses for AY
34 Average Hindsight Method Accident Year Step 1 Calculate projected payment per claim from 24 mos. to ultimate (using results from AY 1997 projection) 34
35 Average Hindsight Method XYZ Auto Insurance Company Calculation of Future Payment per Claim - 24 Months to Ultimate Estimated Number of Number Estimated Paid Estimated Ultimate Closed to Settle Average Accident Ultimate Losses at Future Number Claims at Beyond Future Year Losses 24 Months Payments of Claims 24 Months 24 Mos Payment (1) (2)=see below (3)=Slide 24 (4)=(2)-(3) (5)=Slide 28 (6)=Slide 28 (7)=(5)-(6) (8)=(4)/(7) 1994 $143,820 $97,000 $46, $1, , ,100 60, , , ,100 71, , , ,100 91, ,277 Fitted forecasted value for AY 1998 $2,497 (2) ultimates from Slide 24, 1997 ultimate from Slide 32 35
36 Average Hindsight Method Accident Year Steps 2 & 3 Calculate total future payments for AY 1998 Calculate estimated ultimate losses for AY
37 Average Hindsight Method XYZ Auto Insurance Company Estimated Ultimate Losses: Accident Year 1998 (1) Forecasted Average Future Payment [Slide 35] $2,497 (2) Number of Future Claims to Settle [Slide 28] (Ultimate - Closed Claims) = (3) Estimated Future Loss Payments [ (1) x (2) ] $115,684 (4) Paid Losses to Date [Slide 24] $233,400 (5) Estimated Ultimate Losses [ (3) + (4) ] $349,084 37
38 Average Hindsight Method Steps to Project Accident Year 1999 Ultimate Loss (1) Calculate projected payment per claim from 12 mos. to ultimate (using results from AY s 1997 & 1998 projections) (2) Calculate total future payments for AY 1999 (3) Calculate estimated ultimate losses for AY
39 Average Hindsight Method Accident Year Step 1 (1) Calculate projected payment per claim from 12 mos. to ultimate (using results from AY s 1997 & 1998 projections) 39
40 Average Hindsight Method XYZ Auto Insurance Company Calculation of Future Payment per Claim - 12 Months to Ultimate Estimated Number of Number Estimated Paid Estimated Ultimate Closed to Settle Average Accident Ultimate Losses at Future Number Claims at Beyond Future Year Losses 12 Months Payments of Claims 12 Months 12 Mos Payment (1) (2)=see below (3)=Slide 24 (4)=(2)-(3) (5)=Slide 28 (6)=Slide 28 (7)=(5)-(6) (8)=(4)/(7) 1995 $180,525 $75,500 $105, $1, ,372 91, , , , , , , , , , ,194 Fitted forecasted value for AY 1999 $2,399 (2) ultimates from Slide 24, 1997 from Slide 32, 1998 from Slide 37 40
41 Average Hindsight Method Accident Year Steps 2 & 3 Calculate total future payments for AY 1999 Calculate estimated ultimate losses for AY
42 Average Hindsight Method XYZ Auto Insurance Company Estimated Ultimate Losses: Accident Year 1999 (1) Forecasted Average Future Payment [Slide 40] $2,399 (2) Number of Future Claims to Settle [Slide 28] (Ultimate - Closed Claims) = (3) Estimated Future Loss Payments [ (1) x (2) ] $251,902 (4) Paid Losses to Date [Slide 24] $181,100 (5) Estimated Ultimate Losses [ (3) + (4) ] $433,002 42
43 Average Hindsight Method 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 43
44 AVERAGE INCREMENTAL PAID METHOD 44
45 Average Incremental Paid Method Summary: Estimate the expected ultimate losses for recent accident years based on average incremental paid values per claim. 45
46 Average Incremental Paid Method Data Needed: Ultimate Claim Counts Incremental Paid Loss Triangle 46
47 Average Incremental Paid Method XYZ Auto Insurance Company Cumulative Number of Closed Claims Accident Months of Development Year Ultimate Ultimate claim counts derived in average hindsight method - Slide 28 47
48 Average Incremental Paid Method XYZ Auto Insurance Company Incremental Paid Losses ($000) Accident Months of Development Year $50.0 $30.0 $18.2 $9.6 $5.4 $4.0 $ column = Slide 24, column 3 (24 mos) - column 2 (12 mos) 48
49 Average Incremental Paid Method 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 49
50 Average Incremental Paid Method Step 1 Create triangle of incremental paid losses per ultimate claim 50
51 Average Incremental Paid Method XYZ Auto Insurance Company Incremental Paid Losses per Ultimate Claim (Actual) Accident Months of Development Year Slide 48 (incremental paid losses) / Slide 47 (ultimate claims counts) 51
52 Average Incremental Paid Method Step 2 Calculate incremental payment trend factors and select projected trend factor. 52
53 Average Incremental Paid Method XYZ Auto Insurance Company Incremental Paid Losses per Ultimate Claim (Actual) Accident Months of Development Year /93 9.4% 11.4% 7.3% 15.4% -0.8% -0.1% 1995/94 9.9% 6.2% 9.6% 10.6% 27.7% 1996/95 9.8% 11.7% 11.0% -1.6% 1997/96 8.7% 8.7% 11.0% 1998/ % 8.8% 1999/98 9.1% Select 9.0% 9.0% 9.0% 9.0% 9.0% 9.0% 9.0% 6.2% = 355 / = Slide 51 (1995) / Slide 51 (1994)
54 Average Incremental Paid Method Step 3 Calculate on-level incremental payments [Trend all incremental paid amounts to current (2000) level] 54
55 Average Incremental Paid Method XYZ Auto Insurance Company Incremental Paid Losses per Ultimate Claim (On-Level) Accident Months of Development Year Select N/A = 334 x (1.09) ^ 5 = Slide 51 * (Slide 53) ^ number of years 55
56 Average Incremental Paid Method Step 4 Project future payment amounts [Fill-in the triangle] 56
57 Average Incremental Paid Method XYZ Auto Insurance Company Incremental Paid Losses per Ultimate Claim (Projected) Accident Months of Development Year Total ,179 Slide 55, Selected 83 = 70 x (1.09) ^ 2 = 1996 value x (Slide 53 ^ number of years) Total = Sum across row (projected future severity) 57
58 Average Incremental Paid Method Step 5 Calculate estimated ultimate losses. 58
59 Average Incremental Paid Method XYZ Auto Insurance Company Projected Ultimate Losses Projected Paid Loss Projected Projected Projected Ultimate Accident Per Ult. Claim Future Average Ultimate Losses Year as of 12/99 Severity Severity Claims (000's) (1) (2)=see below (3)=Slide 57 (4)=(2)+(3) (5)=Slide 47 (6)=(4)x(5) 1993 $1,197 $0 $1, $ , , , , , , , , , , ,179 2, (2) = Slide 51, summed across row 59
60 Average Incremental Paid Method Advantages Allows separate analysis of frequency and severity trends Can be modified to account for changes affecting accident year severity (e.g. deductibles, benefit changes) Model can accommodate different trends by accident year, calendar year or development age. Disadvantages Very dependent upon estimate of future inflation rates Less accurate for low frequency lines of business Could be distorted if payout patterns change 60
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