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: United Services Automobile Asn 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 | 0.932 | 0.947 | 0.957 | 0.983 | 0.988 | 0.993 | 0.994 | 0.996 | 0.996 |
| CDF to ult. | 0.803 | 0.862 | 0.910 | 0.951 | 0.968 | 0.979 | 0.986 | 0.992 | 0.996 |
Ultimates & IBNR (Mack stochastic model)
| Origin year | Latest | CDF | Ultimate | IBNR | Mack s.e. | CV |
|---|---|---|---|---|---|---|
| AY 1 | 893,764 | 1.000 | 893,764 | 0 | 0 | 0.0% |
| AY 2 | 989,663 | 0.996 | 985,296 | -4,367 | 907 | -20.8% |
| AY 3 | 1,086,891 | 0.992 | 1,077,957 | -8,934 | 1,417 | -15.9% |
| AY 4 | 1,151,469 | 0.986 | 1,135,524 | -15,945 | 1,930 | -12.1% |
| AY 5 | 1,253,181 | 0.979 | 1,226,920 | -26,261 | 5,560 | -21.2% |
| AY 6 | 1,378,086 | 0.968 | 1,333,337 | -44,749 | 15,859 | -35.4% |
| AY 7 | 1,438,025 | 0.951 | 1,367,608 | -70,417 | 27,152 | -38.6% |
| AY 8 | 1,417,382 | 0.910 | 1,289,717 | -127,665 | 62,891 | -49.3% |
| AY 9 | 1,418,105 | 0.862 | 1,222,449 | -195,656 | 82,773 | -42.3% |
| AY 10 | 1,326,522 | 0.803 | 1,065,258 | -261,264 | 96,031 | -36.8% |
| Total | 12,353,088 | 11,597,830 | -755,258 | 160,799 | -21.3% |
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.