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: California Cas 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 | 2.465 | 1.439 | 1.212 | 1.103 | 1.057 | 1.032 | 1.021 | 1.016 | 1.002 |
| CDF to ult. | 5.382 | 2.183 | 1.517 | 1.252 | 1.135 | 1.073 | 1.040 | 1.019 | 1.002 |
Ultimates & IBNR (Mack stochastic model)
| Origin year | Latest | CDF | Ultimate | IBNR | Mack s.e. | CV |
|---|---|---|---|---|---|---|
| AY 1 | 51,939 | 1.000 | 51,939 | 0 | 0 | 0.0% |
| AY 2 | 46,229 | 1.002 | 46,342 | 113 | 295 | 260.6% |
| AY 3 | 53,956 | 1.019 | 54,955 | 999 | 783 | 78.3% |
| AY 4 | 66,566 | 1.040 | 69,217 | 2,651 | 974 | 36.8% |
| AY 5 | 59,437 | 1.073 | 63,786 | 4,349 | 1,032 | 23.7% |
| AY 6 | 50,742 | 1.135 | 57,583 | 6,841 | 994 | 14.5% |
| AY 7 | 45,580 | 1.252 | 57,070 | 11,490 | 1,204 | 10.5% |
| AY 8 | 44,045 | 1.517 | 66,813 | 22,768 | 1,699 | 7.5% |
| AY 9 | 31,474 | 2.183 | 68,709 | 37,235 | 2,435 | 6.5% |
| AY 10 | 9,372 | 5.382 | 50,439 | 41,067 | 3,626 | 8.8% |
| Total | 459,340 | 586,854 | 127,514 | 7,017 | 5.5% |
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.