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: FL Farm Bureau Grp — Private Passenger Auto (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 | 0.910 | 0.980 | 0.989 | 0.993 | 0.994 | 0.999 | 0.999 | 1.000 | 1.001 |
| CDF to ult. | 0.870 | 0.956 | 0.975 | 0.986 | 0.992 | 0.998 | 0.999 | 1.000 | 1.001 |
Ultimates & IBNR (Mack stochastic model)
| Origin year | Latest | CDF | Ultimate | IBNR | Mack s.e. | CV |
|---|---|---|---|---|---|---|
| AY 1 | 205,997 | 1.000 | 205,997 | 0 | 0 | 0.0% |
| AY 2 | 227,651 | 1.001 | 227,779 | 128 | 54 | 41.9% |
| AY 3 | 260,842 | 1.000 | 260,863 | 21 | 129 | 626.8% |
| AY 4 | 267,632 | 0.999 | 267,406 | -226 | 140 | -61.7% |
| AY 5 | 291,705 | 0.998 | 291,127 | -578 | 169 | -29.2% |
| AY 6 | 313,454 | 0.992 | 311,052 | -2,402 | 671 | -27.9% |
| AY 7 | 350,261 | 0.986 | 345,193 | -5,068 | 1,095 | -21.6% |
| AY 8 | 376,371 | 0.975 | 367,017 | -9,354 | 2,550 | -27.3% |
| AY 9 | 390,974 | 0.956 | 373,639 | -17,335 | 5,250 | -30.3% |
| AY 10 | 444,654 | 0.870 | 386,796 | -57,858 | 10,082 | -17.4% |
| Total | 3,129,541 | 3,036,867 | -92,674 | 12,387 | -13.4% |
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.