To investigate the price fluctuation mechanism of stock markets, this research aims to develop a novel stochastic financial model based on Potts dynamics and compound Poisson process. The new model considers two aspects: information interaction among traders and the uncertain events outside the system. Then, three different volatility statistics (return series $r_t$, absolute return series $|r_t|$ and volatility duration average intensity $V_t$) are introduced to explore the volatility and complexity properties of the proposed model. The descriptive statistical methods, power-law analysis are studied to validate the practicable of the proposed stochastic financial model. The Permutation Lempel-Ziv complexity of moving average series are referred to different volatility sequences to evaluate the complexity of the simulative data from proposed model and the real data from stock market. Moreover, the complexity analysis of Fractional sample entropy and Multiscale fractional sample entropy method are improved to illustrate the complexity of volatility behaviors in different scales. Compared with the real stock data, the empirical results demonstrate that the new model could reproduce the fluctuation and volatility behaviors of real stock markets to some extent.