TITLE:
Catastrophe Risk Derivatives: A New Approach
AUTHORS:
Mehdi Bekralas Abdessalem, Masamitsu Ohnishi
KEYWORDS:
Compound Poisson Process; Extreme Value Theory; Esscher Transform; Index Correction
JOURNAL NAME:
Journal of Mathematical Finance,
Vol.4 No.1,
January
21,
2014
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 amount’s 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.