Analyzing and Predicting CAT Bond Premiums: a Financial Loss Premium Principle and Extreme Value Modeling

CAT bonds play an important role in transferring insurance risks to the capital market. It has been observed that typical CAT bond premiums have changed since the recent financial crisis, which has been attributed to market participants being increasingly risk-averse. In this work, we first propose a new premium principle, the financial loss premium principle, which includes a term measuring losses in the financial market that we represent here by the Conditional Tail Expectation (CTE) of the negative daily log-return of the S&P 500 index. Our analysis of empirical evidence suggests indeed that in the post-crisis market, instead of simply increasing the fixed level of risk load universally, the increased risk aversion should be modeled jointly by a fixed level of risk load and a financial loss factor to reflect trends in the financial market. This new premium principle is shown to be flexible with respect to the confidence/exceedance level of CTE. In the second part, we focus on the particular example of extreme wildfire risk. The distribution of the amount of precipitation in Fort McMurray, Canada, which is a very important factor in the occurrence of wildfires, is analyzed using extreme value modeling techniques. A wildfire bond with parametric trigger of precipitation is then designed to mitigate extreme wildfire risk, and its premium is predicted using an extreme value analysis of its expected loss. With an application to the 2016 Fort McMurray wildfire, we demonstrate that the extreme value model is sensible, and we further analyze how our results and construction can be used to provide a design framework for CAT bonds which may appeal to (re)insurers and investors alike.