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: State Farm Mut Grp — Commercial Auto (paid, 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 | 1.921 | 1.284 | 1.140 | 1.066 | 1.038 | 1.016 | 1.009 | 1.007 | 1.016 |
| CDF to ult. | 3.258 | 1.697 | 1.321 | 1.159 | 1.088 | 1.048 | 1.032 | 1.023 | 1.016 |
Ultimates & IBNR (Mack stochastic model)
| Origin year | Latest | CDF | Ultimate | IBNR | Mack s.e. | CV |
|---|---|---|---|---|---|---|
| AY 1 | 193,499 | 1.000 | 193,499 | 0 | 0 | 0.0% |
| AY 2 | 199,997 | 1.016 | 203,124 | 3,127 | 332 | 10.6% |
| AY 3 | 224,078 | 1.023 | 229,193 | 5,115 | 1,187 | 23.2% |
| AY 4 | 204,911 | 1.032 | 211,401 | 6,490 | 1,157 | 17.8% |
| AY 5 | 208,008 | 1.048 | 218,032 | 10,024 | 1,370 | 13.7% |
| AY 6 | 219,345 | 1.088 | 238,547 | 19,202 | 1,814 | 9.4% |
| AY 7 | 212,446 | 1.159 | 246,282 | 33,836 | 3,390 | 10.0% |
| AY 8 | 190,974 | 1.321 | 252,280 | 61,306 | 4,619 | 7.5% |
| AY 9 | 143,590 | 1.697 | 243,622 | 100,032 | 7,233 | 7.2% |
| AY 10 | 75,827 | 3.258 | 247,080 | 171,253 | 12,926 | 7.5% |
| Total | 1,872,675 | 2,283,059 | 410,384 | 18,264 | 4.5% |
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.