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 — 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 | 2.369 | 1.338 | 1.152 | 1.079 | 1.032 | 1.022 | 1.021 | 0.999 | 0.994 |
| CDF to ult. | 4.218 | 1.781 | 1.331 | 1.155 | 1.070 | 1.037 | 1.014 | 0.993 | 0.994 |
Ultimates & IBNR (Mack stochastic model)
| Origin year | Latest | CDF | Ultimate | IBNR | Mack s.e. | CV |
|---|---|---|---|---|---|---|
| AY 1 | 111,727 | 1.000 | 111,727 | 0 | 0 | 0.0% |
| AY 2 | 116,055 | 0.994 | 115,372 | -683 | 428 | -62.6% |
| AY 3 | 113,243 | 0.993 | 112,504 | -739 | 1,046 | -141.5% |
| AY 4 | 124,352 | 1.014 | 126,118 | 1,766 | 2,797 | 158.4% |
| AY 5 | 109,505 | 1.037 | 113,537 | 4,032 | 3,402 | 84.4% |
| AY 6 | 92,374 | 1.070 | 98,870 | 6,496 | 3,316 | 51.0% |
| AY 7 | 82,470 | 1.155 | 95,260 | 12,790 | 4,302 | 33.6% |
| AY 8 | 64,854 | 1.331 | 86,320 | 21,466 | 5,446 | 25.4% |
| AY 9 | 59,141 | 1.781 | 105,311 | 46,170 | 8,915 | 19.3% |
| AY 10 | 40,409 | 4.218 | 170,432 | 130,023 | 22,558 | 17.3% |
| Total | 914,130 | 1,135,451 | 221,321 | 28,795 | 13.0% |
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.