Chain Ladder / Dev¶

Obtain the Cumulative Triangle¶

In the above example, we already have the cumulative paid triangle. If we were given incremental paid, we would have to derive the cumulative paid triangles.

Create an age-to-age LDF triangle¶

Just divide the \(n+1\) term maturity by the \(n\) term maturity (e.g. obtain the 12-24 maturity for 2016 by

\[ \dfrac{\text{AY 2016 24 month Cumulative paid}}{\text{AY 2016 12 month Cumulative paid}} \]

Do the same for all possible maturities and years

Info

For 2017 its not possible, because only 12-month maturity available

Use #aj to select the LDFs for each Maturity¶

It is important to justify your selections, where ever you do them.

Usually you can just take an average, but if you find some patterns that you wish to take into account, you should do that (for example, by taking a latest 3 year average if the previous year show some *weird* values)

Compute the CDFs¶

Just the Cumulative Development factor, to make finding the ultimate values more convenient.

Simply just product all the LDFs to get the 12-ultimate CDF. If you do that for LDFs from 24-36, 36-48 and so on... you will get the 24-ult CDF.

Success

Later, you will find out that the CDFs are very useful in development techniques like Bornhuetter Ferguson, Cape Cod, Case Outstanding and also when we are doing some retroactive testing in the Evaluation of Techniques section.

Use CDFs to develop the year of interest using the latest maturity value.¶

Viola, just multiply.