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 (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 | 1.000 | 0.995 | 1.003 | 0.999 | 1.001 | 1.000 | 1.002 | 1.004 | 1.010 |
| CDF to ult. | 1.014 | 1.014 | 1.019 | 1.017 | 1.018 | 1.017 | 1.016 | 1.014 | 1.010 |
Ultimates & IBNR (Mack stochastic model)
| Origin year | Latest | CDF | Ultimate | IBNR | Mack s.e. | CV |
|---|---|---|---|---|---|---|
| AY 1 | 194,099 | 1.000 | 194,099 | 0 | 0 | 0.0% |
| AY 2 | 201,101 | 1.010 | 203,207 | 2,106 | 410 | 19.5% |
| AY 3 | 226,739 | 1.014 | 229,928 | 3,189 | 807 | 25.3% |
| AY 4 | 207,581 | 1.016 | 210,973 | 3,392 | 1,274 | 37.6% |
| AY 5 | 214,979 | 1.017 | 218,590 | 3,611 | 1,672 | 46.3% |
| AY 6 | 231,958 | 1.018 | 236,173 | 4,215 | 2,337 | 55.5% |
| AY 7 | 243,140 | 1.017 | 247,201 | 4,061 | 2,929 | 72.1% |
| AY 8 | 238,468 | 1.019 | 243,106 | 4,638 | 4,081 | 88.0% |
| AY 9 | 227,353 | 1.014 | 230,613 | 3,260 | 7,204 | 221.0% |
| AY 10 | 220,029 | 1.014 | 223,114 | 3,085 | 9,530 | 308.9% |
| Total | 2,205,447 | 2,237,005 | 31,558 | 15,627 | 49.5% |
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.