Loss Reserving Methods: Chain Ladder and Bornhuetter-Ferguson

Chain Ladder Method

The chain ladder (development) method uses historical loss development patterns to project ultimate losses. From a loss triangle, development factors are calculated at each maturity: f_j = sum of losses at age j+1 divided by sum of losses at age j. Cumulative development factors (CDFs) project immature losses to ultimate. The reserve for each accident year equals the current reported loss times (CDF minus 1). This method assumes past development patterns will continue and works best with stable, high-volume portfolios.

Bornhuetter-Ferguson Method

The Bornhuetter-Ferguson (BF) method blends the chain ladder projection with an a priori expected loss estimate. The BF reserve equals the a priori expected ultimate loss times the proportion of losses still unreported (1 minus 1/CDF). This method is more stable for immature accident years because it does not rely entirely on reported-to-date experience. The BF ultimate equals reported losses plus the BF reserve. Exam STAM frequently presents loss triangles and asks you to compare chain ladder and BF reserve estimates.