Advanced Ratemaking
Advanced Ratemaking is the CAS Exam 8 domain that tests how indicated rates and risk loads are built from loss experience, classification data, trend and development, credibility, catastrophe models, and reinsurance. The exam expects you to choose a defensible method, document every adjustment, and reconcile the actuarial indication with business and regulatory constraints.
Core mechanics
- Build a loss cost from homogeneous exposures: projected loss cost = developed, trended, on-level losses divided by exposures. Development brings losses to ultimate; trend brings them to the future policy period; on-level factors restate historical losses at the current rate level.
- Convert loss cost to a rate with the permissible loss ratio (PLR): indicated rate = projected loss cost / PLR. PLR covers variable expenses, profit, and contingency; fixed expenses per exposure are usually added separately so they are not double counted.
- Credibility-weight the indication. Limited-fluctuation credibility often uses Z = min(1, sqrt(n/n_full)); Bühlmann-Straub uses exposure weights and variance components. Complement with a related class or overall indication only when the complement is credible and comparable.
- For classification ratemaking, GLMs such as Poisson or Tweedie with a log link produce relativities; set a base level, check balance, and test for omitted variables and interactions.
- For catastrophe and excess business, load expected excess losses, reinstatement premiums, and model uncertainty explicitly; avoid counting the same reinsurance recoverable in both loss and expense.
Worked example
Reported losses are 900,000 on 15,000 exposures, development is 1.12, trend is 1.06, on-level is 1.04, and the PLR is 0.65. Reported loss cost is 900,000 / 15,000 = 60. Projected loss cost is 60 × 1.12 × 1.06 × 1.04 = 74.08. The indicated rate is 74.08 / 0.65 = 113.97. If credibility is 0.60 and the complement indication is 100, the credibility-weighted rate is 0.60 × 113.97 + 0.40 × 100 = 108.38. If fixed expenses were excluded from the PLR, add them after this step.
Traps
- Mixing paid and incurred losses, or applying development factors to data already at ultimate.
- Double counting trend or on-level adjustments, especially after a rate change.
- Using a complement without checking similarity, credibility, or data quality.
- Adding fixed expenses after a PLR that already includes them.
- Double counting catastrophe or reinsurance costs in both loss and expense loads.