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 — Workers' Compensation (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 | 1.159 | 0.979 | 0.994 | 0.995 | 0.999 | 0.996 | 1.002 | 1.002 | 0.998 |
| CDF to ult. | 1.119 | 0.965 | 0.986 | 0.992 | 0.997 | 0.998 | 1.002 | 0.999 | 0.998 |
Ultimates & IBNR (Mack stochastic model)
| Origin year | Latest | CDF | Ultimate | IBNR | Mack s.e. | CV |
|---|---|---|---|---|---|---|
| AY 1 | 133,513 | 1.000 | 133,513 | 0 | 0 | 0.0% |
| AY 2 | 161,673 | 0.998 | 161,326 | -347 | 485 | -139.9% |
| AY 3 | 210,204 | 0.999 | 210,094 | -110 | 1,117 | -1012.4% |
| AY 4 | 244,669 | 1.002 | 245,084 | 415 | 2,227 | 536.1% |
| AY 5 | 253,878 | 0.998 | 253,247 | -631 | 2,679 | -424.9% |
| AY 6 | 251,129 | 0.997 | 250,376 | -753 | 2,990 | -396.8% |
| AY 7 | 202,911 | 0.992 | 201,347 | -1,564 | 3,167 | -202.5% |
| AY 8 | 174,496 | 0.986 | 172,036 | -2,460 | 6,566 | -266.9% |
| AY 9 | 143,042 | 0.965 | 138,051 | -4,991 | 9,768 | -195.7% |
| AY 10 | 125,429 | 1.119 | 140,319 | 14,890 | 27,292 | 183.3% |
| Total | 1,900,944 | 1,905,394 | 4,450 | 31,966 | 718.4% |
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.