Abstract: Catastrophe index options are kinds of the most important catastrophe derivatives at present and hence have large potential in China. However, a major obstacle in the usage of this instrument in China is how to price it under given limited market information as there is not yet an actively traded market for it in China. A closed-form formula of the catastrophe index options pricing based on Esscher transformation is proposed in this paper which has a sound theoretical foundation. Three major features of the catastrophe index: jumping, two periods and two caps can be captured by the proposed method. Moreover, the flexibility of Esscher transformation allaws the method to apply to various distributions. Thus formulas of catastrophe index options pricing are obtained under shifted Poisson, shifted Gamma and Wiener processes respectively in this paper. Simulation part compares the different formulas with the standard Black-Scholes theorem as well as historical PCS catastrophe loss indices, which indicates that the shifted Gamma process is a good candidate for the implied stochastic process of the catastrophe index options pricing. The exploration of catastrophe index option and application of our method is of practical relevance in China.

Key words: catastrophe options, Esscher transformation, Shifted Gamma process