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.
| 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 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 |
| CDF to ult. | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 |
Ultimates & IBNR (Mack stochastic model)
| Origin year | Latest | CDF | Ultimate | IBNR | Mack s.e. | CV |
|---|---|---|---|---|---|---|
| AY 1 | 0 | 1.000 | 0 | 0 | — | 0.0% |
| AY 2 | 0 | 1.000 | 0 | 0 | — | 0.0% |
| AY 3 | 0 | 1.000 | 0 | 0 | — | 0.0% |
| AY 4 | 0 | 1.000 | 0 | 0 | — | 0.0% |
| AY 5 | 0 | 1.000 | 0 | 0 | — | 0.0% |
| AY 6 | 0 | 1.000 | 0 | 0 | — | 0.0% |
| AY 7 | 0 | 1.000 | 0 | 0 | — | 0.0% |
| AY 8 | 0 | 1.000 | 0 | 0 | — | 0.0% |
| AY 9 | 0 | 1.000 | 0 | 0 | — | 0.0% |
| AY 10 | 0 | 1.000 | 0 | 0 | — | 0.0% |
| Total | 0 | 0 | 0 | — | 0.0% |
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.