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: Federal 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 | 0.992 | 0.998 | 0.979 | 0.989 | 0.998 | 0.993 | 0.999 | 1.007 | 1.000 |
| CDF to ult. | 0.955 | 0.963 | 0.965 | 0.986 | 0.997 | 0.999 | 1.007 | 1.007 | 1.000 |
Ultimates & IBNR (Mack stochastic model)
| Origin year | Latest | CDF | Ultimate | IBNR | Mack s.e. | CV |
|---|---|---|---|---|---|---|
| AY 1 | 60,516 | 1.000 | 60,516 | 0 | 0 | 0.0% |
| AY 2 | 65,923 | 1.000 | 65,938 | 15 | 239 | 1564.8% |
| AY 3 | 63,904 | 1.007 | 64,370 | 466 | 528 | 113.4% |
| AY 4 | 66,427 | 1.007 | 66,865 | 438 | 576 | 131.4% |
| AY 5 | 78,850 | 0.999 | 78,775 | -75 | 735 | -983.1% |
| AY 6 | 58,348 | 0.997 | 58,173 | -175 | 779 | -444.9% |
| AY 7 | 64,884 | 0.986 | 63,962 | -922 | 1,310 | -142.0% |
| AY 8 | 75,797 | 0.965 | 73,122 | -2,675 | 1,754 | -65.6% |
| AY 9 | 92,033 | 0.963 | 88,599 | -3,434 | 2,743 | -79.9% |
| AY 10 | 97,148 | 0.955 | 92,790 | -4,358 | 6,260 | -143.6% |
| Total | 723,830 | 713,110 | -10,720 | 8,296 | -77.4% |
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.