chain-ladder (development) method

The chain-ladder method is the most basic and widely used reserving technique, and its logic is almost childishly simple: this year's losses will grow the way past years' losses grew. You take the development factors read off the older, mature rows of the triangle and apply them to the younger, immature rows, marching each row forward one step at a time until it reaches its estimated ultimate. The name comes from chaining the link ratios together like links in a chain.

Precisely, the chain-ladder (or development) method estimates ultimate losses by multiplying each accident year's latest cumulative losses by the appropriate loss development factor — the product of all selected age-to-age factors from that age to ultimate, including the tail. The reserve for each year is its estimated ultimate minus what it has already paid (or incurred). For example, if the latest year shows 5.8 million at 12 months and the 12-month LDF is 1.84, the chain ladder estimates ultimate at about 10.7 million and a reserve of about 4.9 million. It works equally on paid or incurred triangles, giving two independent estimates worth comparing.

Chain ladder matters because it is the default, the benchmark every other method is judged against, and it is wonderfully objective — feed it the same triangle and two actuaries get the same answer. But it has a serious weakness exactly where it is most needed: on the newest accident years, where almost all the losses are still in the future, a tiny wobble in the early development data gets multiplied by a huge LDF and produces a wildly unstable estimate. A single large early claim, or a random quiet quarter, can swing the projected ultimate by millions. That instability is the very reason the Bornhuetter-Ferguson and Cape Cod methods exist — they temper the raw chain ladder with an outside expectation.