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Modeling and Pricing of CAT Bonds

Professor: 
Type: 
Master's Thesis
Corporate Partner: 
Twelve Capital AG
Date Published: 
October 6, 2014

This thesis is concerned with the exploration of Japanese earthquake risk based on statistical analysis with the underlying data set being a catalogue of simulated earthquakes in Japan over 10,000 years produced by AIR Worldwide, and with pricing of various fictitious AT bonds covering this threat.

We perform a statistical analysis of Japanese earthquake risk by modeling three main characteristics: loss, magnitude, and depth. By relying on extreme value theory (EVT) and checking the goodness-of-fit of the distribution fitting, we conclude that generalized Pareto distributions are able to describe extreme losses adequately. According to the interpretation of the sample mean excess plot, gamma or Weibull distributions with a shape parameter larger than 1 are sound candidates for modeling magnitude and depth data of the simulated earthquakes when the high threshold in the sample mean excess plot does not give us sufficient data to fit a GPD model. With the help of diagnostic plots we propose that the gamma distribution fitted to the magnitude data of the simulated earthquakes is quite satisfactory, while the Weibull distribution is able to represent the depth data well. Further, we focus on the issue of modeling the dependence between the characteristic parameters by using the concept of copulas. By fitting Archimedean copulas to the variables, we present their joint distributions, which enable us to have a better and more comprehensive understanding of catastrophic earthquake risk in Japan.

The model fitting builds a solid foundation for CAT bond pricing. We establish two pricing techniques: utility indifference pricing and the Cobb–Douglas–Lane functional form. These help us further to price various hypothetical CAT bonds covering Japanese earthquake risk with different trigger types. Moreover, we also undertake a risk analysis of extreme events, in particular for the 3.11 Tohoku earthquake. The results provide an indication of the practical pricing of CAT bonds concerning Japanese earthquake risk. This thesis is concerned with the exploration of Japanese earthquake risk based on statistical analysis with the underlying data set being a catalogue of simulated earthquakes in Japan over 10,000 years produced by AIR Worldwide, and with pricing of various fictitious AT bonds covering this threat.

We perform a statistical analysis of Japanese earthquake risk by modeling three main characteristics: loss, magnitude, and depth. By relying on extreme value theory (EVT) and checking the goodness-of-fit of the distribution fitting, we conclude that generalized Pareto distributions are able to describe extreme losses adequately. According to the interpretation of the sample mean excess plot, gamma or Weibull distributions with a shape parameter larger than 1 are sound candidates for modeling magnitude and depth data of the simulated earthquakes when the high threshold in the sample mean excess plot does not give us sufficient data to fit a GPD model. With the help of diagnostic plots we propose that the gamma distribution fitted to the magnitude data of the simulated earthquakes is quite satisfactory, while the Weibull distribution is able to represent the depth data well. Further, we focus on the issue of modeling the dependence between the characteristic parameters by using the concept of copulas. By fitting Archimedean copulas to the variables, we present their joint distributions, which enable us to have a better and more comprehensive understanding of catastrophic earthquake risk in Japan.

The model fitting builds a solid foundation for CAT bond pricing. We establish two pricing techniques: utility indifference pricing and the Cobb–Douglas–Lane functional form. These help us further to price various hypothetical CAT bonds covering Japanese earthquake risk with different trigger types. Moreover, we also undertake a risk analysis of extreme events, in particular for the 3.11 Tohoku earthquake. The results provide an indication of the practical pricing of CAT bonds concerning Japanese earthquake risk. This thesis is concerned with the exploration of Japanese earthquake risk based on statistical analysis with the underlying data set being a catalogue of simulated earthquakes in Japan over 10,000 years produced by AIR Worldwide, and with pricing of various fictitious AT bonds covering this threat.

We perform a statistical analysis of Japanese earthquake risk by modeling three main characteristics: loss, magnitude, and depth. By relying on extreme value theory (EVT) and checking the goodness-of-fit of the distribution fitting, we conclude that generalized Pareto distributions are able to describe extreme losses adequately. According to the interpretation of the sample mean excess plot, gamma or Weibull distributions with a shape parameter larger than 1 are sound candidates for modeling magnitude and depth data of the simulated earthquakes when the high threshold in the sample mean excess plot does not give us sufficient data to fit a GPD model. With the help of diagnostic plots we propose that the gamma distribution fitted to the magnitude data of the simulated earthquakes is quite satisfactory, while the Weibull distribution is able to represent the depth data well. Further, we focus on the issue of modeling the dependence between the characteristic parameters by using the concept of copulas. By fitting Archimedean copulas to the variables, we present their joint distributions, which enable us to have a better and more comprehensive understanding of catastrophic earthquake risk in Japan.

The model fitting builds a solid foundation for CAT bond pricing. We establish two pricing techniques: utility indifference pricing and the Cobb–Douglas–Lane functional form. These help us further to price various hypothetical CAT bonds covering Japanese earthquake risk with different trigger types. Moreover, we also undertake a risk analysis of extreme events, in particular for the 3.11 Tohoku earthquake. The results provide an indication of the practical pricing of CAT bonds concerning Japanese earthquake risk. This thesis is concerned with the exploration of Japanese earthquake risk based on statistical analysis with the underlying data set being a catalogue of simulated earthquakes in Japan over 10,000 years produced by AIR Worldwide, and with pricing of various fictitious AT bonds covering this threat.

We perform a statistical analysis of Japanese earthquake risk by modeling three main characteristics: loss, magnitude, and depth. By relying on extreme value theory (EVT) and checking the goodness-of-fit of the distribution fitting, we conclude that generalized Pareto distributions are able to describe extreme losses adequately. According to the interpretation of the sample mean excess plot, gamma or Weibull distributions with a shape parameter larger than 1 are sound candidates for modeling magnitude and depth data of the simulated earthquakes when the high threshold in the sample mean excess plot does not give us sufficient data to fit a GPD model. With the help of diagnostic plots we propose that the gamma distribution fitted to the magnitude data of the simulated earthquakes is quite satisfactory, while the Weibull distribution is able to represent the depth data well. Further, we focus on the issue of modeling the dependence between the characteristic parameters by using the concept of copulas. By fitting Archimedean copulas to the variables, we present their joint distributions, which enable us to have a better and more comprehensive understanding of catastrophic earthquake risk in Japan.

The model fitting builds a solid foundation for CAT bond pricing. We establish two pricing techniques: utility indifference pricing and the Cobb–Douglas–Lane functional form. These help us further to price various hypothetical CAT bonds covering Japanese earthquake risk with different trigger types. Moreover, we also undertake a risk analysis of extreme events, in particular for the 3.11 Tohoku earthquake. The results provide an indication of the practical pricing of CAT bonds concerning Japanese earthquake risk.