Abstract: This paper proposes the Bayesian heavy tailed stochastic volatility models with jumps to describe the jumps characteristics in financial market In terms of the volatility models' structure and their state space transition,we construct a Markov Chain Monte Carlo algo rithm to estimate parameters,utilize Kalman filters and Gaussian simulation smoother to analyze the latent volatility implied in models,and compare volatility models through Bayesian factors.Then the suggested approach is applied to analyze the volatility character of the stock market in China and America.The results show that the jump character is significant both in China and America stock market,and the heavy-tailed stochastic volatility model with jumps is superior to the standard volatility model in depicting volatility character.

Key words: stochastic volatility, state space, Kalman Filter, jump process, bayesian factor