coverages. Price “indications” are not transaction prices. Nevertheless, they convey useful information and we incorporate them as a further step in the cross section analysis to further isolate price relationships.

In Section 4, ILW are incorporated into the analysis because we are able to associate an independent estimate of the risk of each ILW with its price “indication”.<sup>6</sup> A remodeling exercise is conducted to homogenize the risk statistics. While a particular ILS prospectus comes with a risk analysis from one of the major modeling companies (AIR Worldwide, RMS or EQECAT) it often only comes with summary statistics and they are not always directly comparable. The remodeling of nearly all ILS by one company allows two important features not previously available, namely a full risk profile for each ILS, and a set of profiles on the same basis. This set of data is used to compute alternative risk and/or capital measures such as Value at Risk and Tail Value at Risk and try to relate these to price.

Finally, the paper concludes with several observations about catastrophe risk pricing and capital allocation, which may be helpful to international financial institutions like the World Bank in structuring its efforts in this new arena. However, the exercise must be viewed as a best preliminary and the first in many such studies. The results are empirical and derived from unique sources and perspectives. As the market matures and progresses it is hoped that more telling insights can be derived as well as better theories of this important area. Hopefully the results herein will stimulate such activity.

# Analysis of the Time Series of Original Issue Statistics

## **_The simple linear model_**

Our objective is to explain ILS pricing and thereby make inference to the impact of capital on price. The pure transaction database available is the set of original issue prices for 247<sup>7</sup> ILS issued since 1997. For each issue there is a known spread over LIBOR<sup>8</sup> (the equivalent of reinsurance premium) and an associated expected loss<sup>9</sup> . So the simple linear model, Model 1, is: _Premium Spread = a + b * (Expected Loss)_ If, in this expression, a=0 then _Spread_ is proportional to _Expected Loss_ . If also _b_ >1 then _Spread_ contains some “load” above _Expected Loss_ . Often rationales for insurance pricing assume that _Premium Spread = Function (Expected Loss, Load, Other Expenses)_ In this expression the load is an amount over cost to generate the risk takers profit. More pointedly, load is to generate return on, or be the cost of, capital. On the ILS market, the investor is typically not confronted with expenses so our focus is on Expected Loss (EL) and Load. If Load is related to return on

> 6 The independent measure is provided courtesy of AIR Worldwide, one of the three independent modeling agencies that regularly provide modeling to ILS prospectuses.

> 7 The actual number of issues to Q1 2008 is actually higher, 251, but certain issues were excluded due to a lack of information or regularity of form.

> 8 The term “Premium Spread” is used to convey the fact that in an ILS the Spread over LIBOR is the equivalent of what Premium would be if the same risk were in reinsurance form. We also use it interchangeably to mean price. 9 Typically, the probability of attachment and exhaustion will also be available to investors, often with some other statistics on perils but we do not examine those here.

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