The catastrophe options distinguish between a loss period [0,T1],during which the catastrophes may happen, and a development period [T1,T2], during which losses entered before T1 are reestimated. In this paper, we will model cumulative catastrophe loss before T1 as a doubly stochastic Poisson process. In order to incorporate the seasonal effect on the occurrence of catastrophe events, we will let both the intensity of Poisson process and the distribution of jump size depend on the state of a continuous time Markov chain. During the development period, losses are reestimated by a geometric Brownian motion. In this setting we derive partial integro-differential equations for the prices of catastrophe options. Using Fourier transform techniques, we are able to provide analytical pricing formulas for catastrophe options.