# **1. Introduction**

Catastrophe models are complex and almost completely inaccessible to the non-specialist. Yet, these models tell policymakers what are the economic risks to society and form the basis of rate making for billions of dollars in insurance premiums per year in the United States alone. We summarize two important results from US hurricane catastrophe models: one for base normal (BN) hurricane risk and one for climate conditioned (CC) hurricane risk. Summary results are presented in Loss Exceedance Curve (LEC) form, which is a kind of cumulative distribution function and thus gives considerable summary information about what hurricane catastrophe models are saying about hurricane risk, both in the absence and in the presence of climate conditioning.

This paper presents a simple method for the comparison of catastrophe model outputs based on a so-called intensity profile (IP) and residual intensity profile (RIP). The IP and RIP are used to compare the catastrophe model risk estimates of BN hurricane risk versus CC hurricane risk. CC hurricane models were implemented by catastrophe modeling companies in 2006 after a series of academic papers and the heightened hurricane activity of 2004 and 2005 gave impetus to the notion that tropical cyclones occur more frequently in the current climactic regime. CC catastrophe models offer the darkest view of U.S. hurricane risk that can be justified from historical observations of North Atlantic hurricanes. Therefore, a comparison of BN versus CC catastrophe models offers a glimpse into the assumed causes and costs of climatically driven increases in hurricane activity. Using our simple method of comparison, we show that CC catastrophe models imply that the recent 30 to 50 years’ worth of climate change has increased North Atlantic hurricane frequency to a level approximately 30% greater than normal. While a significant increase, we put this increase in perspective by pointing out that increases in U.S. coastal property density have exhibited a long-term secular trend of 50% real growth per decade. This means that the total impact of up to 50 years’ worth of climate change on U.S. Hurricane risk is worth less than 10 years’ worth of U.S. coastal property growth. The potential impact on non-U.S. reinsurance markets is a decline in coverage capacity.

# **2.  Catastrophe models are not pricing models**

Before going on to discuss catastrophe models, it is important to emphasize that catastrophe models are not pricing models. The results of catastrophe models do not lead directly to insurance and reinsurance prices, mainly because of the cost of the capital which must be put-up against systemic insurance risks.<sup>2</sup> An in-depth discussion of the issues and reasons behind the incomplete linkage between actuarial estimates of risk and market prices for risk transfer is beyond the scope of this report; however, the reader can gain some understanding to the issue through a simplified example of a reinsurance price function. A reinsurance broker might summarize for insurance clients the cost of reinsurance in a given year with something like the following formula:<sup>3</sup> ROL = LOL + 5%, (1)

> 2 Cummins, J.D. and Olivier Mahul (2009): “Catastrophe Risk Financing in Developing Countries: Principles for Public Intervention.” The International Bank for Reconstruction and Development / The World Bank.

> 3 Cummins and Mahul (2009). See in particular Figure 2.2 on p.35.

2