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 (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 | 1.921 | 1.248 | 1.106 | 1.051 | 1.022 | 1.009 | 1.004 | 1.003 | 1.001 |
| CDF to ult. | 2.894 | 1.507 | 1.207 | 1.091 | 1.038 | 1.016 | 1.007 | 1.003 | 1.001 |
Ultimates & IBNR (Mack stochastic model)
| Origin year | Latest | CDF | Ultimate | IBNR | Mack s.e. | CV |
|---|---|---|---|---|---|---|
| AY 1 | 886,334 | 1.000 | 886,334 | 0 | 0 | 0.0% |
| AY 2 | 982,148 | 1.001 | 982,932 | 784 | 917 | 117.0% |
| AY 3 | 1,075,537 | 1.003 | 1,079,102 | 3,565 | 1,327 | 37.2% |
| AY 4 | 1,138,375 | 1.007 | 1,146,697 | 8,322 | 1,667 | 20.0% |
| AY 5 | 1,226,650 | 1.016 | 1,246,146 | 19,496 | 2,945 | 15.1% |
| AY 6 | 1,324,732 | 1.038 | 1,375,073 | 50,341 | 7,486 | 14.9% |
| AY 7 | 1,320,130 | 1.091 | 1,440,528 | 120,398 | 19,877 | 16.5% |
| AY 8 | 1,185,300 | 1.207 | 1,430,755 | 245,455 | 34,104 | 13.9% |
| AY 9 | 966,162 | 1.507 | 1,455,908 | 489,746 | 63,486 | 13.0% |
| AY 10 | 542,021 | 2.894 | 1,568,804 | 1,026,783 | 118,000 | 11.5% |
| Total | 10,647,389 | 12,612,279 | 1,964,890 | 149,116 | 7.6% |
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.