Reserving Methods Cheat Sheet

Chain Ladder Method

• Age-to-age factor: f_k = sum(C_(i, k+1)) / sum(C_(i, k)) (weighted average)
• Cumulative development factor: CDF_k = f_k * f_(k+1) * ... * f_(ultimate)
• Ultimate losses: Ultimate_i = C_(i, current) * CDF_(current age)
• IBNR: IBNR_i = Ultimate_i - Paid_i (or Incurred_i)

Bornhuetter-Ferguson Method

• Expected losses: EL_i = Earned Premium_i * Expected Loss Ratio
• Percent unreported: q_i = 1 - 1/CDF_i
• BF Ultimate: Ultimate_i = Reported_i + EL_i * q_i
• BF IBNR: IBNR_i = EL_i * q_i

Cape Cod Method

• Used-up premium: UP_i = EP_i * (1/CDF_i)
• Expected loss ratio: ELR = sum(Reported_i) / sum(UP_i)
• Cape Cod Ultimate: Ultimate_i = Reported_i + EP_i * ELR * q_i

When to Use Each Method

• Chain Ladder: Best when development patterns are stable and historical data is credible
• Bornhuetter-Ferguson: Better for immature accident years with little development data
• Cape Cod: Good compromise when expected loss ratios are uncertain