1999 casualty loss reserve seminar intermediate track ii - techniques
DESCRIPTION
1999 CASUALTY LOSS RESERVE SEMINAR Intermediate Track II - Techniques. SEPTEMBER 1999. RESERVE MODELS. Average Hindsight Reserve Method (Slides 2 - 12) Average Incremental Paid Method (Slides 13 - 19) Bornhuetter-Ferguson Method (Slides 20 - 30) Slide 1. - PowerPoint PPT PresentationTRANSCRIPT
1999 CASUALTY LOSS RESERVE SEMINAR
Intermediate Track II - Techniques
SEPTEMBER 1999
RESERVE MODELS
Average Hindsight Reserve Method (Slides 2 - 12)
Average Incremental Paid Method (Slides 13 - 19)
Bornhuetter-Ferguson Method (Slides 20 - 30)
Slide 1
AVERAGE HINDSIGHT RESERVE METHOD
Goal: Estimate The Average Future Settlement Value Per Claim For . Recent Accident Years, Both For Claims Already Reported . and Future Claim Reports
Based On: Projected Ultimate Losses and Hindsight . Average Values For More Mature Accident Years
Hindsight (Current Ultimate-Historical Payments) is the . Implied Unpaid Amount
Slide 2
AVERAGE HINDSIGHT RESERVE METHOD
Data Needed
Cumulative Paid Loss Triangle
Cumulative Closed (Paid) Claim Count Triangle
Estimated Ultimate Number of Claims for All Accident Years
Estimated Ultimate Losses For Several Mature Accident Years
Slide 3
AVERAGE HINDSIGHT RESERVE METHOD
XYZ Auto Insurance Company
Cumulative Paid Losses ($000)
Accident Months Of Development .
Year 12 24 36 48 60 72 84 Ultimate
1992 $50.0 $80.0 $98.2 $107.8 $113.2 $117.2 $119.7 $119.7
1993 60.2 97.0 118.5 130.7 136.6 141.0 143.8
1994 75.5 120.1 147.0 162.4 171.0 178.7
1995 91.9 147.1 180.2 197.0 220.1
1996 115.0 184.1 226.4 *
1997 146.5 233.4 *
1998 181.1 *
*To be estimated
Slide 4
AVERAGE HINDSIGHT RESERVE METHOD
XYZ Auto Insurance Company
Cumulative Number Of Closed Claims
Accident Months Of Development .
Year 12 24 36 48 60 72 84 Ultimate*
1992 50 75 88 94 97 99 100 100
1993 55 83 97 104 107 109 110
1994 63 94 110 118 122 125
1995 70 105 123 131 140
1996 80 120 141 160
1997 93 139 185
1998 105 210
*Estimated using claim count development factors.
Slide 5
AVERAGE HINDSIGHT RESERVE METHOD
XYZ Auto Insurance Company
Calculation Of Average Outstanding Losses At 36 Months
Purpose: Project Future Settlement Dollars For 1996
Number
Estimated Estimated Number of to Settle Average
Estimated Paid Future Ultimate Closed Beyond Future
Accident Ultimate Losses at Payments Number Claims at 36 Mos* Payment . Year Losses 36 Months = (2)-(3) of Claims 36 Months =(5)-(6) =(4)/(7)
(1) (2) (3) (4) (5) (6) (7) (8)
1992 $119,700 $98,200 $21,500 100 88 12 $1,792
1993 143,800 118,500 25,300 110 97 13 1,946
1994 178,700 147,000 31,700 125 110 15 2,113
1995 220,100 180,200 39,900 140 123 17 2,347
*Includes IBNR Claims Fitted forecasted value for AY 1996 = $2,549
Slide 6
AVERAGE HINDSIGHT RESERVE METHOD
XYZ Auto Insurance Company
Estimated Ultimate Losses: Accident Year 1996
(1) Forecasted Average Future Payment [Slide 6] = $2,549
(2) Number of Future Claims to Settle [Slide 5]
(Ultimate - Closed Claims) = 160 - 141 = 19
(3) Estimated Future Loss Payments [(1) x (2)] = $ 48,431
(4) Paid Losses to Date [Slide 4] = $226,400
(5) Estimated Ultimate Losses [(3) + (4)] = $274,831
Slide 7
AVERAGE HINDSIGHT RESERVE METHOD
XYZ Auto Insurance Company
Calculation Of Average Outstanding Losses At 24 Months
Purpose: Project Future Settlement Dollars For 1997
Number
Estimated Estimated Number of to Settle Average
Estimated Paid Future Ultimate Closed Beyond Future
Accident Ultimate Losses at Payments Number Claims at 24 Mos* Payment . Year Losses 24 Months = (2)-(3) of Claims 24 Months =(5)-(6) =(4)/(7)
(1) (2) (3) (4) (5) (6) (7) (8)
1993 $143,800 $97,000 $46,800 110 83 27 $1,733
1994 178,700 120,100 58,600 125 94 31 1,890
1995 220,100 147,100 73,000 140 105 35 2,086
1996 274,831 184,100 90,731 160 120 40 2,268
*Includes IBNR Claims Fitted forecasted value for AY 1997 = $2,484
Slide 8
AVERAGE HINDSIGHT RESERVE METHOD
XYZ Auto Insurance Company
Estimated Ultimate Losses: Accident Year 1997
(1) Forecasted Average Future Payment [Slide 8] = $2,484
(2) Number of Future Claims to Settle [Slide 5]
(Ultimate - Closed Claims) = 185 - 139 = 46
(3) Estimated Future Loss Payments [(1) x (2)] = $ 114,264
(4) Paid Losses to Date [Slide 4] = $233,400
(5) Estimated Ultimate Losses [(3) + (4)] = $347,664
Slide 9
AVERAGE HINDSIGHT RESERVE METHOD
XYZ Auto Insurance Company
Calculation Of Average Outstanding Losses At 12 Months
Purpose: Project Future Settlement Dollars For 1998
Number
Estimated Estimated Number of to Settle Average
Estimated Paid Future Ultimate Closed Beyond Future
Accident Ultimate Losses at Payments Number Claims at 12 Mos* Payment . Year Losses 12 Months = (2)-(3) of Claims 12 Months =(5)-(6) =(4)/(7)
(1) (2) (3) (4) (5) (6) (7) (8)
1994 $178,700 $75,500 $103,200 125 63 62 $1,665
1995 220,100 91,900 128,200 140 70 70 1,831
1996 274,831 115,000 159,831 160 80 80 1,998
1997 347,664 146,500 201,164 185 93 92 2,187
*Includes IBNR Claims Fitted forecasted value for AY 1998 = $2,397
Slide 10
AVERAGE HINDSIGHT RESERVE METHOD
XYZ Auto Insurance Company
Estimated Ultimate Losses: Accident Year 1998
(1) Forecasted Average Future Payment [Slide 10] = $2,397
(2) Number of Future Claims to Settle [Slide 5]
(Ultimate - Closed Claims) = 210 - 105 = 105
(3) Estimated Future Loss Payments [(1) x (2)] = $ 251,385
(4) Paid Losses to Date [Slide 4] = $181,100
(5) Estimated Ultimate Losses [(3) + (4)] = $432,785
Slide 11
AVERAGE HINDSIGHT RESERVE METHOD
ADVANTAGES
Relatively Unaffected by Changes in Case Reserving Practices Can Easily Adjust Trend Assumption 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 (Example: Retentions Dramatically Increase) Too “Formula” Driven
Slide 12
AVERAGE INCREMENTAL PAID METHOD
Incremental Paid Losses per Ultimate Claim (Actual)
Accident Months Of Development .
Year 0-12 12-24 24-36 36-48 48-60 60-72 72-84
1992 500 300 182 96 54 40 25
1993 547 335* 195 111 54 40
1994 604 357 215 123 69
1995 656 394 236 120
1996 719 432 264
1997 792 470
1998 862
* 335 = (97,000-60,200) / 110
(Slide 4 @ 24 months -Slide 4 @ 12 months) / Slide 5 Ultimate
Slide 13
AVERAGE INCREMENTAL PAID METHOD
Trend Factors
Accident Months Of Development .
Year 0-12 12-24 24-36 36-48 48-60 60-72 72-84
1993/92 9.4% 11.7% 7.1% 15.6% 0.0% 0.0%
1994/93 10.4% 6.6%* 10.3% 10.8% 27.8%
1995/94 8.6% 10.4% 9.8% - 2.4%
1996/95 9.6% 9.6% 11.9%
1997/96 10.2% 8.8%
1998/97 8.8%
Select 9.0% 9.0% 9.0% 9.0% 9.0% 9.0% 9.0%
* 6.6% = 357 / 335 - 1
Slide 13 (1994) / Slide 13 (1993) - 1
Slide 14
AVERAGE INCREMENTAL PAID METHOD
Incremental Paid Losses per Ultimate Claim (On-level)
Accident Months Of Development .
Year 0-12 12-24 24-36 36-48 48-60 60-72 72-84
1992 914 503 280 136 70 48 27
1993 917 515* 275 144 64 44
1994 929 504 278 146 75
1995 926 510 280 131
1996 931 513 288
1997 941 512
1998 940
Select N/A 510 280 140 70 46 27
* 515 = 335 x (1.09 ^ 5)
Slide 13 x (Slide 14 ^ number of years) Slide 15
AVERAGE INCREMENTAL PAID METHOD
Incremental Paid Losses per Ultimate Claim (Projected)
Accident Months Of Development .
Year 0-12 12-24 24-36 36-48 48-60 60-72 72-84 Total
1992 0
1993 27 27
1994 46 29 75
1995 70 50 32 152
1996 140 76 55 35 306
1997 280 152 83* 60 38 613
1998 510 305 166 91 65 42 1,179
* 83 = 70 x (1.09 ^ 2)
= 1994 value x (Slide 14 ^ number of years)
Slide 16
AVERAGE INCREMENTAL PAID METHOD
Projected Ultimate Losses
(1) (2) (3) (4) (5)
Paid Loss Projected Projected Projected Projected
Per Ult. Claim Future Ultimate Ultimate Ultimate
Accident as of Severity Severity Claims Losses ($000)
. Year 12/31/98 (Slide 16) (1) + (2) (Slide 5) (3) x (4)
1992 $1,197 $0 $1,197 100 $119.7
1993 1,282 27 1,309 110 144.0
1994 1,368 75 1,443 125 180.4
1995 1,407 152 1,559 140 218.3
1996 1,415 306 1,721 160 275.4
1997 1,262 613 1,875 185 346.9
1998 862 1,179 2,041 210 428.6
(1) = Slide 13, summed across row Slide 17
AVERAGE INCREMENTAL PAID METHOD
Summary
Step 1: Project Ultimate Claims
Step 2: Calculate Historical Severities
Step 3: Select Trend Factor
Step 4: Calculate On-level Severities
Step 5: Select On-level Severities
Step 6: Project Future Severities
Step 7: Multiply Total Severities by Ultimate Claims
Slide 18
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.
Slide 19
BORNHEUTTER-FERGUSON METHOD
Data Needed
Earned Premium or Exposure By Year
A priori Expected Loss Ratio or Pure Premium For Each Year
An Estimate of the Percent of Dollars Unreported, Usually . Based on Loss Development Factors (LDFs)
Slide 20
BORNHUETTER-FERGUSON METHOD“IBNR” RESERVES
As of the evaluation date, there are four categories of future claims activity that . may not be reflected in either claim payments or case reserves.
1. Losses Not Yet Reported To The Company
2. Claims In Transit (Reported But Not Recorded)
3. Future Development On Known Open Claims
4. Reopenings on Claims Currently Closed
The Bornhuetter-Ferguson method and most accident year methods estimate “broad” IBNR which includes all four categories.
NOTE: The sum of (1) and (2) is termed “True” or “Pure” IBNR.
Slide 21
BORNHUETTER-FERGUSON METHODBasic Formulas
Expected Losses = Loss Ratio x Earned Premium
= Pure Premium x Exposure
= Frequency x Severity
IBNR Reserve = IBNR Factor x Expected Losses
Slide 22
BORNHUETTER-FERGUSON METHODXYZ Auto Insurance Company
Accident Year .
1996 1997 1998
(1) Earned Premium $1,250 $1,600 $2,000
(2) Expected Loss Ratio 65% 70% 75%
(3) Initial Expected Losses (1) x (2) $813 $1,120 $1,500
(4) Development Factor 1.350 1.650 2.000
(5) IBNR Factor [1 - [1 / (4)] 26% 39% 50%
(6) IBNR Reserve (3) x (5) $211 $437 $750
(7) Reported Losses at 12/31/98 $600 $700 $1,000
(8) Estimated Ultimate Losses (6) + (7) $811 $1,137 $1,750
Slide 23
BORNHUETTER-FERGUSON METHODIBNR Factor Derivation
IBNR Factor = IBNR / Ultimate Losses
= Ultimate - Incurred to Date
Ultimate
= 1.000 - (Incurred to Date/Ultimate)
= 1.000 - [1.000/(LDF-to-Ultimate)]
= 1.000 - Percent Unreported
= Percent Unreported
Slide 24
BORNHUETTER-FERGUSON METHOD
XYZ Auto Insurance Company
Accident Year .
1996 1997 1998
(1) Ultimate Losses
a. Expected (Slide 23, Line 3) 813 1,120 1,500
b. Estimated (Slide 23, Line 8) 811 1,137 1,750
(2) Reported Losses at 12/31/98
a. Expected (Slide 23, Line 3 - Line 6) 602 683 750
b. Actual 600 700 1,000
(3) Loss Ratio
a. Expected (Slide 23, Line 2) 65.0% 70.0% 75.0%
b. Estimated (Slide 23, Line 8/Line 1) 64.9% 71.1% 87.5%
Slide 25
BORNHEUTTER-FERGUSON METHOD
Considerations
Premium Adequacy and Expected Loss Ratios
- Sources: pricing assumptions, historical data such as Schedule P, industry data Changes in Operations:
- Reinsurance
- Longer-Tailed Lines (LDF selection more critical)
- Underlying Limits, Deductibles
- Claims Made versus Occurrence
- Claims Handling Changes in Mix of Business That May Impact Either Loss Ratios, and/or Development Patterns
Slide 26
BORNHUETTER-FERGUSON METHOD
Advantages
Easy to Use Compromises Between Loss Development and Expected Loss
Ratio Methods Avoids 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
Disadvantages Depends on Expected Loss Ratio or A Priori Pure Premium Requires Development Factors
Slide 27
BORNHUETTER-FERGUSON METHOD
XYZ Auto Insurance Company
Illustration Of Tempering Effect
One Extra
Large Claim
Expected of $150
EXPECTED LOSS RATIO METHOD
(1) Earned Premium $2,000 $2,000
(2) Expected Loss Ratio 75% 75%
(3) Projected Ultimate Losses (1) x (2) $1,500 $1,500
LOSS DEVELOPMENT METHOD
(4) Actual Reported to Date $750 $900
(5) Development Factor 2.00 2.00
(6) Projected Ultimate Losses (4) x (5) $1,500 $1,800
Slide 28
BORNHUETTER-FERGUSON METHOD
XYZ Auto Insurance Company
Illustration Of Tempering Effect
One Extra
Large Claim
Expected of $150
BORNHUETTER-FERGUSON METHOD
(1) Earned Premium $2,000 $2,000
(2) Expected Loss Ratio 75% 75%
(3) Expected Ultimate Losses (1) x (2) $1,500 $1,500
(4) Actual Reported to Date $750 $900
(5) Development Factor 2.00 2.00
(6) IBNR Factor 1 - [1 / (5)] 50% 50%
(7) Projected Ultimate Losses $1,500 $1,650
(4) + [(3) x (6)]
Slide 29
BORNHUETTER-FERGUSON METHOD
XYZ Auto Insurance Company
Illustration Of “Tempering” Effect
One Extra
Large Claim
Method Expected of $150
(1) Expected Loss Ratio Method $1,500 $1,500
(2) Loss Development $1,500 $1,800
(3) Bornhuetter-Ferguson $1,500 $1,650
Slide 30