PROCEEDINGS May 15, 16, 17, 18, 2005 - Casualty Actuarial Society

ARCHITECTURE FOR RESIDENTIAL PROPERTY INSURANCE RATEMAKING 505Since and T in formula (3) are not observed directly, this isthe practical formula for the total non-loss portion of reinsurancecosts. 11The fixed reinsurance cost provision from typical data is derivedin Exhibit 4. Direct earned premiums for the line, the portionsubject to the cat reinsurance program, modeled gross annuallosses, and actual cat reinsurance premiums ceded to varioussources are compiled. The reinsured portion of modeled losses isderived by subtracting the retention (often based on subject premium)and the losses not covered due to coinsurance features ofthe treaty (typically 5% of losses above the retention). The actualceded premium is normally significantly larger than this amount,and the difference represents cost of capital and transaction costs.For the overall rate level indication, the fixed reinsurance costsare expressed as a ratio to direct earned premium. In addition, itis useful later to think of these costs as a load to the gross cededlosses or “capacity charge” per dollar of expected loss. The fixedcost provision is carried to Exhibit 1.Note that the ceded premiums are specific to the line of businessunder review. In practice, ceded cat reinsurance premiumsare rarely specified by line, only in aggregate. The actuary mustassist accountants in allocating the ceded premiums to line ofbusiness. Exhibit 5 provides an example. Direct earned premiumsby line are compiled, with the property portion extractedfor (currently) “indivisible” premium lines of business. This becomesthe subject premium for most cat reinsurance programs.The portion due to property perils must be estimated from losscost data. The actual all-lines ceded premium is allocated to linebased on the modeled gross annual losses, separable by line from11 The astute reader will note that the “blended” formula is actually incomplete. There isno cost of capital levied on the internal capital held for retained catastrophic losses. In aheavily reinsured company, we can ignore this part of the capital charge for simplicityof presentation. Obviously, the formula cost of capital for an insurer which retainedall losses and built a risk load into rates directly would not be zero. This presentationassumes that the bulk of cat losses are ceded and that the associated cost of capital isrevealed by the market.