Tail Estimation and Catastrophe Security Pricing: Can We Tell What Target We Hit if We Are Shooting in the Dark?

The past few years have seen the development and growth of traded securities with payoffs tied to natural disasters. With this comes a need for tools to evaluate the underlying risks involved. Pricing the insurance features imbedded in these securities is difficult and imprecise. This lack of pricing precision translates into greater required return premiums to holders of these securities This paper explores the nature of pricing uncertainty for a number of data sets, security designs, and loss distributions using mathematical techniques for assessing small-sample variance. Specifically the techniques applied are known as "jackknife" and "bootstrap" and where invented by the statistician John Tukey in the 1950's. The paper contains nearly 50 tables and graphs detailing the findings. Finally, the economic impact of pricing uncertainty is then briefly explored. It is shown that while differences between distribution assumption may not generate statistically significant differences in loss estimates, the economic difference in prices that these different distributions generate is large. The author asserts that while reinsurers will currently place "big bets" based on relatively small amounts of information, it will become more important to develop better understanding of the actual size of these risks as issuers seek to spread them to more entities through the capital markets. He concludes that the more confidently we can state what the price of a risky security "should" be, the more attractive these securities will become and the more successful they will be as investments and means of sharing risk.