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: Canal Ins Co Grp — Commercial Auto (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 | 0.948 | 0.969 | 0.983 | 0.955 | 0.942 | 0.938 | 0.947 | 0.923 | 0.915 |
| CDF to ult. | 0.609 | 0.642 | 0.663 | 0.674 | 0.706 | 0.749 | 0.799 | 0.844 | 0.915 |
Ultimates & IBNR (Mack stochastic model)
| Origin year | Latest | CDF | Ultimate | IBNR | Mack s.e. | CV |
|---|---|---|---|---|---|---|
| AY 1 | 27,491 | 1.000 | 27,491 | 0 | 0 | 0.0% |
| AY 2 | 27,548 | 0.915 | 25,196 | -2,352 | 488 | -20.8% |
| AY 3 | 31,849 | 0.844 | 26,875 | -4,974 | 1,035 | -20.8% |
| AY 4 | 39,510 | 0.799 | 31,577 | -7,933 | 2,206 | -27.8% |
| AY 5 | 43,396 | 0.749 | 32,524 | -10,872 | 2,533 | -23.3% |
| AY 6 | 56,883 | 0.706 | 40,145 | -16,738 | 3,229 | -19.3% |
| AY 7 | 68,518 | 0.674 | 46,172 | -22,346 | 3,960 | -17.7% |
| AY 8 | 74,040 | 0.663 | 49,066 | -24,974 | 4,290 | -17.2% |
| AY 9 | 75,357 | 0.642 | 48,366 | -26,991 | 4,282 | -15.9% |
| AY 10 | 67,622 | 0.609 | 41,158 | -26,464 | 4,065 | -15.4% |
| Total | 512,214 | 368,569 | -143,645 | 15,821 | -11.0% |
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.