The Chain-Ladder is an reserving technique often used to predict future claims for an insurance company.
It uses run-off triangle of paid or incurred losses. There are several considerations as not to distort the numbers, for instance changes in premium. This subject can be made arbitrary complex however for the purpose in this text we assume that this has been handled and we focus on the practical steps to be taken,
The claims might be listed on an accumulated basis or a year-by-year basis. Let’s assume that the above table has the accumulated paid claims.
- The rows represents accident years.
- The columns represents development years.
As an example during 2015 there was claims of 1,000 paid for accident year 2018. One year later there was additional claims of 200 paid for accident year 2018. Summing up to 1,200 in total. After the third year we assume that the claims are fully developed and will not increase more. However for 2015 and 2016 we will calculate predictions.
The basic idea is to calculate development factors. They represent growth (usually an increase) from one year to the next.
The first development factor is calculated as (1,200+700)/(1,000+500)=1.27
The next development factor is calculated as (1,400)/(1,200)=1.17
This estimates the claims at A to be A = 700*1.17 = 817
And the claims at B to be B = 200*1.27 = 253
And the claims at C to be C = 200*1.27*1.17 = 296
As at end of 2017 the reserve required to pay future claims would be A+C = 1,112.
As a heads-up below or some reasons why the observed claims patterns may need further consideration before applying the Chain-Ladder method:
Changes in product design and conditions.
Changes in the claims reporting, assessment and settlement processes.
Changes in the legal environment.
Abnormally large or small claim settlement amounts.