Pricing the Impact of Adjustable Features and Loss Sharing Provisions of Reinsurance Treaties

Many excess-of-loss reinsurance contracts contain non-proportional coinsurance clauses, where the ceding company is to pay a non-proportional share of losses without receiving a commensurate share of the reinsurance premium. Such clauses include aggregate deductibles, loss ratio caps or limited reinstatements, and loss corridor provisions. Quite frequently in the broker market, and less frequently in the direct market, excess-of-loss treaties will contain adjustable premium or commission features. These adjustable features include retrospective rating plans, profit commission or profit sharing plans, and sliding scale commission plans. This paper compares two alternate approaches to pricing several relatively common treaty examples, the lognormal aggregate loss model and the Heckman-Meyers Collective Risk Model. These comparisons suggest that the lognormal model provides a satisfactory approximation to the theoretically more appropriate Collective Risk Model results when use of the latter more sophisticated procedure is not warranted due to resource limitations. Thus, application of the lognormal model can lead to significant efficiency gains in reinsurance price monitoring work and in pricing situations where limited information is available. Appendices summarize important excess-of-loss pricing methodologies and provide an expanded lognormal table.