By comparing four different stochastic volatility models, this paper attempted to find out whether the extreme realizations out of a stock market return time series can be interpreted as a tail behavior of a non-Gaussian distribution, or as the superimposition of a jump component on a Gaussian diffusion, or as a phenomenon in which both forces are at work within the same data generating process. An empirical study of Shanghai stock composition index daily returns data shows that China's Shanghai stock market volatility is characterized by obvious leptokurtic (fat-tail) and lower persistence. In addition, the jump parameters can be estimated precisely due to enough excess returns, which means the stock market is heavily affected by various related government policies. And model comparisons between the two return series show that SV models with a jump component can sufficiently describe a return time series with dramatic moves, not one with mild volatility.