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 (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 | 1.040 | 0.998 | 0.985 | 1.005 | 1.002 | 1.001 | 0.995 | 1.005 | 0.932 |
| CDF to ult. | 0.962 | 0.925 | 0.926 | 0.940 | 0.935 | 0.933 | 0.932 | 0.937 | 0.932 |
Ultimates & IBNR (Mack stochastic model)
| Origin year | Latest | CDF | Ultimate | IBNR | Mack s.e. | CV |
|---|---|---|---|---|---|---|
| AY 1 | 122,959 | 1.000 | 122,959 | 0 | 0 | 0.0% |
| AY 2 | 138,113 | 0.932 | 128,768 | -9,345 | 959 | -10.3% |
| AY 3 | 141,400 | 0.937 | 132,483 | -8,917 | 1,500 | -16.8% |
| AY 4 | 158,833 | 0.932 | 148,044 | -10,789 | 2,332 | -21.6% |
| AY 5 | 145,693 | 0.933 | 135,999 | -9,694 | 4,498 | -46.4% |
| AY 6 | 135,266 | 0.935 | 126,541 | -8,725 | 5,185 | -59.4% |
| AY 7 | 137,863 | 0.940 | 129,590 | -8,273 | 5,565 | -67.3% |
| AY 8 | 148,799 | 0.926 | 137,821 | -10,978 | 9,469 | -86.3% |
| AY 9 | 172,063 | 0.925 | 159,082 | -12,981 | 12,726 | -98.0% |
| AY 10 | 196,269 | 0.962 | 188,806 | -7,463 | 15,083 | -202.1% |
| Total | 1,497,258 | 1,410,093 | -87,165 | 29,980 | -34.4% |
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.