chain-ladder method
{{Short description|Loss reserving method in actual science}}
The chain-ladder or development{{Cite web |last=Friedland |first=Jacqueline |date=July 30, 2010 |title=Estimating Unpaid Claims Using Basic Techniques |url=https://www.casact.org/sites/default/files/database/studynotes_friedland_estimating.pdf |website=Casualty Actuarial Society}} method is a prominent{{cite journal | doi=10.1007/BF02808592 | volume=24 | title=Chain Ladder Prediction and Asset Liability Management | journal=Blätter der DGVFM | pages=1–9| year=1999 | last1=Schmidt | first1=Klaus D. | s2cid=167794128 }}{{Cite web | url=http://www.investopedia.com/terms/c/chain-ladder-method-clm.asp | title=Chain Ladder Method (CLM)}} actuarial loss reserving technique.
The chain-ladder method is used in both the property and casualty{{Cite web |last=Werner |first=Geoff |last2=Modlin |first2=Claudine |last3=Willis Towers Watson |date=May 2016 |title=Basic Ratemaking |url=https://www.casact.org/sites/default/files/old/studynotes_werner_modlin_ratemaking.pdf |website=Casualty Actuarial Society}} and health insurance{{cite web |title=Valuation and Reserving Techniques |url=http://www.soa.org/files/pd/health/hspring07-005bk.pdf |url-status=dead |archiveurl=https://web.archive.org/web/20140327110448/http://www.soa.org/files/pd/health/hspring07-005bk.pdf |archivedate=2014-03-27 |accessdate=2016-03-13}} fields. Its intent is to estimate incurred but not reported claims and project ultimate loss amounts.
The primary underlying assumption of the chain-ladder method is that historical loss development patterns are indicative of future loss development patterns.
Methodology
According to Jacqueline Friedland's "Estimating Unpaid Claims Using Basic Techniques," there are seven steps to apply the chain-ladder technique:
- Compile claims data in a development triangle
- Calculate age-to-age factors
- Calculate averages of the age-to-age factors
- Select claim development factors
- Select tail factor
- Calculate cumulative claim development factors
- Project ultimate claims
Age-to-age factors, also called loss development factors (LDFs) or link ratios, represent the ratio of loss amounts from one valuation date to another, and they are intended to capture growth patterns of losses over time. These factors are used to project where the ultimate amount losses will settle.
Example
Firstly, losses (either reported or paid) are compiled into a triangle, where the rows represent accident years and the columns represent valuation dates. For example, the entry '43,169,009' represents loss amounts related to claims occurring in 1998, valued as of 24 months.
| class="wikitable"
! {{diagonal split header| ! 12 !! 24 !! 36 !! 48 !! 60 !! 72 !! 84 !! 96 !! 108 !! 120 |
| 1998
| 37,017,487 || 43,169,009 || 45,568,919 || 46,784,558 || 47,337,318 || 47,533,264 || 47,634,419 || 47,689,655 || 47,724,678 || 47,742,304 |
|---|
| 1999
| 38,954,484 || 46,045,718 || 48,882,924 || 50,219,672 || 50,729,292 || 50,926,779 || 51,069,285 || 51,163,540 || 51,185,767 || |
| 2000
| 41,155,776 || 49,371,478 || 52,358,476 || 53,780,322 || 54,303,086 || 54,582,950 || 54,742,188 || 54,837,929 || || |
| 2001
| 42,394,069 || 50,584,112 || 53,704,296 || 55,150,118 || 55,895,583 || 56,156,727 || 56,299,562 || || || |
| 2002
| 44,755,243 || 52,971,643 || 56,102,312 || 57,703,851 || 58,363,564 || 58,592,712 || || || || |
| 2003
| 45,163,102 || 52,497,731 || 55,468,551 || 57,015,411 || 57,565,344 || || || || || |
| 2004
| 45,417,309 || 52,640,322 || 55,553,673 || 56,976,657 || || || || || || |
| 2005
| 46,360,869 || 53,790,061 || 56,786,410 || || || || || || || |
| 2006
| 46,582,684 || 54,641,339 || || || || || || || || |
| 2007
| 48,853,563 || || || || || || || || || |
Next, age-to-age factors are determined by calculating the ratio of losses at subsequent valuation dates. From 24 months to 36 months, accident year 1998 losses increased from 43,169,009 to 45,568,919, so the corresponding age-to-age factor is 45,568,919 / 43,169,009 = 1.056. A "tail factor" is selected (in this case, 1.000) to project from the latest valuation age to ultimate.
| class="wikitable"
! Accident year ! 12-24 !! 24-36 !! 36-48 !! 48-60 !! 60-72 !! 72-84 !! 84-96 !! 96-108 !! 108-120 !! To ult |
| 1998
| 1.166 || 1.056 || 1.027 || 1.012 || 1.004 || 1.002 || 1.001 || 1.001 || 1.000 || |
|---|
| 1999
| 1.182 || 1.062 || 1.027 || 1.010 || 1.004 || 1.003 || 1.002|| 1.000 || || |
| 2000
| 1.200 || 1.061 || 1.027 || 1.010 || 1.005 || 1.003 || 1.002 || || || |
| 2001
| 1.193 || 1.062 || 1.027 || 1.014 || 1.005 || 1.003 || || || || |
| 2002
| 1.184 || 1.059 || 1.029 || 1.011 || 1.004 || || || || || |
| 2003
| 1.162 || 1.057 || 1.028 || 1.010 || || || || || || |
| 2004
| 1.159 || 1.055 || 1.026 || || || || || || || |
| 2005
| 1.160 || 1.056 || || || || || || || || |
| 2006
| 1.173 || || || || || || || || || |
| 2007
| || || || || || || || || || |
Finally, averages of the age-to-age factors are calculated. Judgmental selections are made after observing several averages. The age-to-age factors are then multiplied together to obtain cumulative development factors.
| class="wikitable"
! {{diagonal split header| ! 12-24 !! 24-36 !! 36-48 !! 48-60 !! 60-72 !! 72-84 !! 84-96 !! 96-108 !! 108-120 !! To ult |
| Simple average last 5 years
| 1.168 || 1.058 || 1.027 || 1.011 || 1.004 || 1.003 || 1.002 || 1.001 || 1.000 || |
|---|
| Simple average last 3 years
| 1.164 || 1.056 || 1.027 || 1.012 || 1.005 || 1.003 || 1.002 || 1.001 || 1.000 || |
| Volume weighted last 5 years
| 1.168 || 1.058 || 1.027 || 1.011 || 1.004 || 1.003 || 1.002 || 1.001 || 1.000 || |
| Volume weighted last 3 years
| 1.164 || 1.056 || 1.027 || 1.012 || 1.005 || 1.003 || 1.002 || 1.001 || 1.000 || |
| Selected
| 1.164 || 1.056 || 1.027 || 1.012 || 1.005 || 1.003 || 1.002 || 1.001 || 1.000 || 1.000 |
| Cumulative to ultimate
| 1.292 || 1.110 || 1.051 || 1.023 || 1.011 || 1.006 || 1.003 || 1.001 || 1.000 || 1.000 |
The cumulative development factors multiplied by the reported (or paid) losses to project ultimate losses.
Incurred but not reported can be obtained by subtracting reported losses from ultimate losses, in this case, 569,172,456 - 543,481,587 = 25,690,869.{{Cite conference |last=Schmidt |first=Klaus D. |date=September 11–12, 2006 |title=Methods and Models of Loss Reserving Based on Run-Off Triangles: A Unifying Survey |url=https://www.casact.org/sites/default/files/database/forum_06fforum_273.pdf |conference=2006 CAS Casualty Loss Reserve Seminar}}
Limitations
The chain-ladder technique is only accurate when patterns of loss development in the past can be assumed to continue in the future. In contrast to other loss reserving methods such as the Bornhuetter–Ferguson method, it relies only on past experience to arrive at an incurred but not reported claims estimate.
When there are changes to an insurer's operations, such as a change in claims settlement times, changes in claims staffing, or changes to case reserve practices, the chain-ladder method will not produce an accurate estimate without adjustments.
The chain-ladder method is also very responsive to changes in experience, and as a result, it may be unsuitable for very volatile lines of business.
See also
References
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