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 — 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 | 2.486 | 1.336 | 1.138 | 1.067 | 1.024 | 1.025 | 1.013 | 1.008 | 1.003 |
| CDF to ult. | 4.337 | 1.745 | 1.306 | 1.148 | 1.076 | 1.050 | 1.025 | 1.012 | 1.003 |
Ultimates & IBNR (Mack stochastic model)
| Origin year | Latest | CDF | Ultimate | IBNR | Mack s.e. | CV |
|---|---|---|---|---|---|---|
| AY 1 | 60,516 | 1.000 | 60,516 | 0 | 0 | 0.0% |
| AY 2 | 65,511 | 1.003 | 65,733 | 222 | 679 | 306.4% |
| AY 3 | 62,626 | 1.012 | 63,363 | 737 | 958 | 130.0% |
| AY 4 | 64,518 | 1.025 | 66,121 | 1,603 | 1,129 | 70.4% |
| AY 5 | 74,048 | 1.050 | 77,781 | 3,733 | 1,499 | 40.2% |
| AY 6 | 53,599 | 1.076 | 57,656 | 4,057 | 1,415 | 34.9% |
| AY 7 | 54,388 | 1.148 | 62,453 | 8,065 | 1,767 | 21.9% |
| AY 8 | 49,835 | 1.306 | 65,105 | 15,270 | 5,228 | 34.2% |
| AY 9 | 44,377 | 1.745 | 77,432 | 33,055 | 7,828 | 23.7% |
| AY 10 | 27,309 | 4.337 | 118,442 | 91,133 | 44,656 | 49.0% |
| Total | 556,727 | 714,600 | 157,873 | 46,707 | 29.6% |
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.