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: State Farm Mut 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 | 1.796 | 1.194 | 1.086 | 1.040 | 1.020 | 1.010 | 1.005 | 1.003 | 1.001 |
| CDF to ult. | 2.517 | 1.401 | 1.174 | 1.081 | 1.039 | 1.019 | 1.009 | 1.004 | 1.001 |
Ultimates & IBNR (Mack stochastic model)
| Origin year | Latest | CDF | Ultimate | IBNR | Mack s.e. | CV |
|---|---|---|---|---|---|---|
| AY 1 | 6,815,646 | 1.000 | 6,815,646 | 0 | 0 | 0.0% |
| AY 2 | 7,712,077 | 1.001 | 7,719,821 | 7,744 | 3,993 | 51.6% |
| AY 3 | 8,364,955 | 1.004 | 8,396,601 | 31,646 | 6,439 | 20.3% |
| AY 4 | 8,215,810 | 1.009 | 8,288,545 | 72,735 | 7,184 | 9.9% |
| AY 5 | 8,876,813 | 1.019 | 9,043,728 | 166,915 | 11,582 | 6.9% |
| AY 6 | 9,337,099 | 1.039 | 9,702,726 | 365,627 | 26,930 | 7.4% |
| AY 7 | 9,640,098 | 1.081 | 10,422,621 | 782,523 | 45,938 | 5.9% |
| AY 8 | 9,006,113 | 1.174 | 10,571,471 | 1,565,358 | 71,929 | 4.6% |
| AY 9 | 7,486,113 | 1.401 | 10,490,872 | 3,004,759 | 146,613 | 4.9% |
| AY 10 | 4,344,144 | 2.517 | 10,933,658 | 6,589,514 | 508,539 | 7.7% |
| Total | 79,798,868 | 92,385,689 | 12,586,821 | 550,736 | 4.4% |
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.