Chain-Ladder Development
Project ultimate losses from a loss-development triangle using selectable age-to-age averaging methods, an optional fitted tail, and Mack (1993) standard errors.
Loaded: Taylor & Ashe (1983) — General Liability (classic textbook triangle) (incurred, CAS Loss Reserve DB)
| Origin \ Dev | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| AY 1 | ||||||||||
| AY 2 | ||||||||||
| AY 3 | ||||||||||
| AY 4 | ||||||||||
| AY 5 | ||||||||||
| AY 6 | ||||||||||
| AY 7 | ||||||||||
| AY 8 | ||||||||||
| AY 9 | ||||||||||
| AY 10 |
Development factors
| Age | 1→2 | 2→3 | 3→4 | 4→5 | 5→6 | 6→7 | 7→8 | 8→9 | 9→10 |
|---|---|---|---|---|---|---|---|---|---|
| Method | |||||||||
| Factor | 3.491 | 1.747 | 1.457 | 1.174 | 1.104 | 1.086 | 1.054 | 1.077 | 1.018 |
| CDF to ult. | 14.447 | 4.139 | 2.369 | 1.625 | 1.384 | 1.254 | 1.155 | 1.096 | 1.018 |
Ultimates & IBNR (Mack stochastic model)
| Origin year | Latest | CDF | Ultimate | IBNR | Mack s.e. | CV |
|---|---|---|---|---|---|---|
| AY 1 | 3,901,463 | 1.000 | 3,901,463 | 0 | 0 | 0.0% |
| AY 2 | 5,339,085 | 1.018 | 5,433,719 | 94,634 | 75,535 | 79.8% |
| AY 3 | 4,909,315 | 1.096 | 5,378,826 | 469,511 | 121,699 | 25.9% |
| AY 4 | 4,588,268 | 1.155 | 5,297,906 | 709,638 | 133,549 | 18.8% |
| AY 5 | 3,873,311 | 1.254 | 4,858,200 | 984,889 | 261,406 | 26.5% |
| AY 6 | 3,691,712 | 1.384 | 5,111,171 | 1,419,459 | 411,010 | 29.0% |
| AY 7 | 3,483,130 | 1.625 | 5,660,771 | 2,177,641 | 558,317 | 25.6% |
| AY 8 | 2,864,498 | 2.369 | 6,784,799 | 3,920,301 | 875,328 | 22.3% |
| AY 9 | 1,363,294 | 4.139 | 5,642,266 | 4,278,972 | 971,258 | 22.7% |
| AY 10 | 344,014 | 14.447 | 4,969,825 | 4,625,811 | 1,363,155 | 29.5% |
| Total | 34,358,090 | 53,038,946 | 18,680,856 | 2,447,095 | 13.1% |
IBNR by origin year with Mack std. error
Assumptions & limitations
- Development patterns are stable across origin years and future development follows the same age-to-age factors as historical experience.
- Mack's model assumes the chain-ladder recursion is correctly specified (uncorrelated origin years, no calendar-year trend) and factors are the volume-weighted averages unless overridden per age.
- A fitted exponential-decay tail is an extrapolation; validate against industry benchmarks before relying on it.