This paper investigates the pricing of CatEPuts under
a Markovian regime-switching jump-diffusion model. The parameters of this model,
including the risk-free interest rate, the appreciation rate and the volatility
of the clients' equity, are modulated by a continuous-time, finite-state, observable
Markov chain. An equivalent martingale measure is selected by employing the
regime-switching Esscher transform. The fast Fourier transform (FFT) technique
is applied to price the CatEPuts. In a two-state Markov chain case, numerical
example is presented to illustrate the practical implementation of the model.