Category: Actuarial fundamentals · Reviewed by Taylor Watts, Broker · New Business · Last reviewed
Chain ladder method
The chain ladder method is the most widely used deterministic loss-development technique. Given a loss triangle, it estimates ultimate losses by extending the diagonal using age-to-age development factors derived from the observed historical pattern.
Algorithm
Tabulate cumulative paid or incurred losses in a triangle.
Compute age-to-age factors: f(j, j+1) = Σ C(i, j+1) / Σ C(i, j) for each development period pair.
Project the latest diagonal forward by successive application of factors.
Ultimate = projected value at the final development column.
No major calendar-year effects (legal change, court rulings, inflation shocks).
Violations of these assumptions are the main source of chain-ladder error. Practitioners almost always supplement with Bornhuetter-Ferguson for recent immature years.
Stochastic chain ladder
Mack’s model (1993) — distribution-free standard error of the chain-ladder reserve estimate.
Bootstrap chain ladder — re-sampling-based simulation of reserve distributions.
Over-dispersed Poisson GLM — yields chain-ladder point estimates with statistical inference.
These extensions support Solvency II technical provisions and ORSA stress testing.
References
Mack, T. (1993). Distribution-free calculation of the standard error of chain ladder reserve estimates. ASTIN Bulletin 23(2).
England, P.D. and Verrall, R.J. (1999). Analytic and bootstrap estimates of prediction errors in claims reserving. Insurance: Mathematics and Economics 25.
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