Claims reserve calculator
Pick a published UK claims triangle. The calculator projects every accident year to its final cost using the chain ladder method, measures the uncertainty, and checks the method against what was actually paid.
Paste your own triangle
One row per accident year, the year label first, then amounts by development year. Leave future cells blank. Copying straight from Excel works.
The triangle
Development factors
Each figure shows how much an accident year's paid total grew from one year to the next. The selected factor for each column is applied to every year still developing. Click any figure to leave it out, for example a one-off large claim.
Results by accident year
Would this method have worked?
The test hides the most recent payments, runs the same method on what was known before, and compares its forecast with what was actually paid.
Three years later: the 2021 report against what happened
Direct Line's report for 2021 and its report for 2024 overlap for accident years 2015 to 2021. That shows how both forecasts made in 2021 have held up: this calculator's chain ladder and the insurer's own best estimate.
The insurer's estimates are its gross undiscounted best estimate claims provisions from the same template, so the comparison is on its own consistent basis.
How sensitive is the answer?
Method, data and limits
The calculation
- Link ratios. For each accident year, paid at development year k+1 divided by paid at year k.
- Selected factor. Volume-weighted: the column total at k+1 divided by the column total at k, over the same accident years. Simple: the average of the link ratios.
- Projection. Each accident year's latest paid amount is multiplied by the remaining factors and the tail factor to give its final cost.
- Reserve. Final cost minus paid so far.
- Uncertainty. Mack's (1993) standard error, which measures how much the chain ladder estimate could vary given the scatter in the link ratios. Shown when no tail factor is used.
Every number is checked by automated tests against the open-source chainladder library maintained by the Casualty Actuarial Society, and against Mack's published results.
The data
What this does not do
- Paid triangles miss claims that are reported but not yet paid, so they react late to change.
- Ten development years end before the longest injury claims settle. The insurer's estimate allows for those; chain ladder does not unless you add a tail factor.
- The Direct Line triangles combine motor, home, commercial and other lines. Real reserving splits them, because each develops differently.
- Amounts are gross of reinsurance and undiscounted.