The Complementary Compound Truncated Poisson-Weibull Distribution for Pricing Catastrophic Bonds for Extreme Earthquakes

Aims: This paper aims at bridging the gap or managing the level of overall losses between economic losses and insured losses that are usually caused by extreme earthquakes, by calculating the price of catastrophic bonds. While examining the frequency of the event, it was observed that, at least, one accident occurred periodically, which resulted in maximum losses.

Study Design: This study is an empirical research based on maximum losses that are due to earthquake events per year, as obtained from the International Disaster Database and Munich Re.

Place and Duration of Study: The study analyzed 80 extreme earthquake events in the world, between 1906 and 2015.

Methodology: The Complementary risk method used in calculating a mixed probability distribution expresses the number of earthquakes and the maximum losses realized. Zero truncated Poisson distribution is used for frequency distribution and Last order Weibull distribution for losses. The data were analyzed using IBM SPSS (Statistical Package for Social Sciences) Statistics 22 and MathCad 2001 professional software.

Results: It was discovered that the maximum losses of earthquake were fitted with compound truncated Poisson-Weibull distribution. Expected values have been calculated for extreme earthquake losses, which exceed the specific descriptive measures. The expected values of extreme losses caused by earthquakes are a net premium, present value or net price of the catastrophic bonds. It was observed that the present value of catastrophic bonds decreases as the retention increases. Risk management of natural disaster (by transferring the losses to the financial markets) is one of the derivative methods considered as an alternative or complement to traditional insurance. The process of transferring losses to capital markets through the catastrophic bonds (to cover natural disasters) leads to greater coverage of these losses, by maintaining that natural disaster losses are relative to the size of the capital markets, and are less than the ratio to the size of the insurance markets, in addition to the possibility of providing the necessary funds for reconstruction.