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 (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 | 2.684 | 1.342 | 1.156 | 1.082 | 1.051 | 1.027 | 1.023 | 1.013 | 1.013 |
| CDF to ult. | 5.112 | 1.904 | 1.419 | 1.227 | 1.134 | 1.079 | 1.050 | 1.026 | 1.013 |
Ultimates & IBNR (Mack stochastic model)
| Origin year | Latest | CDF | Ultimate | IBNR | Mack s.e. | CV |
|---|---|---|---|---|---|---|
| AY 1 | 125,049 | 1.000 | 125,049 | 0 | 0 | 0.0% |
| AY 2 | 147,358 | 1.013 | 149,216 | 1,858 | 474 | 25.5% |
| AY 3 | 187,760 | 1.026 | 192,674 | 4,914 | 893 | 18.2% |
| AY 4 | 213,396 | 1.050 | 224,115 | 10,719 | 1,399 | 13.0% |
| AY 5 | 213,904 | 1.079 | 230,811 | 16,907 | 1,847 | 10.9% |
| AY 6 | 193,676 | 1.134 | 219,624 | 25,948 | 2,383 | 9.2% |
| AY 7 | 151,081 | 1.227 | 185,415 | 34,334 | 2,496 | 7.3% |
| AY 8 | 111,268 | 1.419 | 157,873 | 46,605 | 2,855 | 6.1% |
| AY 9 | 66,033 | 1.904 | 125,746 | 59,713 | 4,292 | 7.2% |
| AY 10 | 25,265 | 5.112 | 129,150 | 103,885 | 18,210 | 17.5% |
| Total | 1,434,790 | 1,739,672 | 304,882 | 20,578 | 6.7% |
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.