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Catastrophe Risk Derivatives: A New Approach

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DOI: 10.4236/jmf.2014.41003    3,691 Downloads   5,932 Views   Citations

ABSTRACT

The multiplication of disasters during the last two decades beside the urbanism expansion has made catastrophe claims grow dramatically. Against a priced reinsurance, catastrophe derivative products became ever more attractive to insurance companies. A robust pricing of these derivatives is based on an appropriate modeling of the loss index. The current study proposes a unique model that takes into account the statistical characteristics of the loss amounts tails to assess its real distribution. Thus, unlike previous models, we elaborately do not make any assumption regarding the probability of jump sizes to facilitate the calculation of the option price but deduct it instead of using Extreme Value Theory. The core of our model is a jump process that allows later for loss amounts re-estimation. Using both the Esscher transform and the martingale approach, we present the price of a call option on the loss index in a closed form. Finally, to confirm the underpinning theory of the model, numerical examples are presented as well as an algorithm that can be used to derive the option prices in real time.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

M. Abdessalem and M. Ohnishi, "Catastrophe Risk Derivatives: A New Approach," Journal of Mathematical Finance, Vol. 4 No. 1, 2014, pp. 21-34. doi: 10.4236/jmf.2014.41003.

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