LDF: Loss development factor
Ratio of cumulative losses at two successive development ages, the building block of the chain ladder method.
A loss development factor (LDF, or age-to-age factor) is the ratio of cumulative losses at one development age to cumulative losses at the prior age, for the same accident year. LDF(n→n+1) = Cumulative(n+1) / Cumulative(n). On a loss development triangle, LDFs are calculated for each accident year and each column, then averaged (simple average, weighted average, median) to arrive at selected factors. Those are chained together to give the CDF, the cumulative development factor to ultimate. An LDF close to 1 means little development is left; a high LDF signals a long-tail line. Reading LDFs accident year by accident year helps spot shifts in claims patterns or unusual losses.
Textbook case, on a motor liability triangle: LDF 12→24 months = 1.45; LDF 24→36 = 1.18; LDF 36→48 = 1.07; LDF 48→ultimate = 1.02. CDF from 12 months = 1.45 × 1.18 × 1.07 × 1.02 ≈ 1.87.
loss development factor, age-to-age factor, link ratio, LDF
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