where ROL is “rate on line,” the reinsurance premium divided by the limit of coverage, and LOL is “loss on line,” the average annual loss (AAL) of a reinsurance contract divided by the limit of coverage. The AAL is the expected annual loss averaged over a long period of time. It is typically gotten from a catastrophe model, which performs detailed, stochastic scenario analyses, as will be discussed further in the next section below. Putting aside taxes, overhead, and other transactional costs, if reinsurance premiums were purely determined by actuarial risk, the additional 5% term in (1) would not exist: ROL would equal to LOL in a world with no cost of capital and no transaction costs.

The impact of catastrophe model changes most often has a muted impact on insurance and reinsurance premiums, which is supported well by the form of price functional illustrated by (1). For example, the LOL might vary by up to 30% up or down from model to model (so a 1% LOL in one model might be 1.3% in another, equally valid model<sup>4</sup> ), but the excess premium represented by the 5% term in (1) might range anywhere from 3% to 12% year to year, depending on the cost of insurance and reinsurance capital in a given year.<sup>5</sup> This means, especially for catastrophic risks which have a low probability of occurrence, the majority of the year-to-year volatility in reinsurance prices might be attributed to factors outside of the variation in risk estimates produced by catastrophe models.

All of this is not to say that catastrophe models do not matter. They matter a great deal because they form the basis of a market-driven conversation on prices and availability of insurance and reinsurance. Also, too, catastrophe models potentially form a constructive link between science, engineering, and commerce. By their integration into the global insurance and reinsurance market, catastrophe models subject scientific developments in meteorology and seismology to an intense examination, the results of which are disseminated annually into a market that involves hundreds of billions of dollars in premiums worldwide. When this model-based system of commerce functions as intended, risk is taken more deliberately and with the costs and benefits more clearly in mind.

# **3.  Catastrophe models**

Catastrophe models are specialized computer models6 that use probabilistic scenario analysis to provide estimates of the probability of different size losses occurring in well-defined insurance systems. Catastrophe models first emerged in the late 1980s as affordable computing power 4 The most commonly asked question (what is the characteristic model uncertainty in catastrophe models) is typically unanswered by modeling firms. Generalizations are difficult to come by. Model uncertainty varies according the hazard being modeled. In case of U.S. hurricane risks, a reasonable estimate of model uncertainty is plus or minus 30%. So, for example, if an event is judged to have an annual probability of occurrence of 1% by one modeler, another, equally expert modeler, might estimate the probability of occurrence of the same event at 1.3% and yet another, equally expert modeler, might estimate the probability of occurrence of the same event at .7%. More typically, the variance among expert opinion in U.S. hurricane would be expected to be closer to plus or minus 15%, so the plus or minus 30% range is intended to encompass a wide range of variance in expert opinion.

5 In the Spring of 2009, in the reinsurance market for US hurricane risks, the ROL is anywhere from 8 to 12% for a 1% LOL.

6 Commercial models include those from Applied Insurance Research (AIR), EQECAT, Risk Management Solutions (RMS). Public domain models include the FEMA HAZUS model by Applied Research Associates (ARA) as well as the Florida Office of Insurance Regulation’s Florida Public Hurricane Model.

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