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: Canal Ins Co Grp — Commercial Auto (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 | 1.952 | 1.216 | 1.095 | 1.047 | 1.011 | 1.003 | 0.995 | 1.002 | 1.001 |
| CDF to ult. | 2.755 | 1.411 | 1.160 | 1.060 | 1.012 | 1.001 | 0.998 | 1.003 | 1.001 |
Ultimates & IBNR (Mack stochastic model)
| Origin year | Latest | CDF | Ultimate | IBNR | Mack s.e. | CV |
|---|---|---|---|---|---|---|
| AY 1 | 27,445 | 1.000 | 27,445 | 0 | 0 | 0.0% |
| AY 2 | 27,470 | 1.001 | 27,504 | 34 | 1 | 3.5% |
| AY 3 | 30,004 | 1.003 | 30,092 | 88 | 23 | 26.1% |
| AY 4 | 33,727 | 0.998 | 33,643 | -84 | 491 | -583.1% |
| AY 5 | 39,237 | 1.001 | 39,271 | 34 | 708 | 2074.9% |
| AY 6 | 53,350 | 1.012 | 53,980 | 630 | 1,302 | 206.6% |
| AY 7 | 60,726 | 1.060 | 64,354 | 3,628 | 1,594 | 43.9% |
| AY 8 | 54,432 | 1.160 | 63,159 | 8,727 | 1,805 | 20.7% |
| AY 9 | 42,563 | 1.411 | 60,074 | 17,511 | 2,386 | 13.6% |
| AY 10 | 21,074 | 2.755 | 58,055 | 36,981 | 3,659 | 9.9% |
| Total | 390,028 | 457,578 | 67,550 | 6,787 | 10.0% |
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.