This paper investigates high frequency time-series features of stock returns and volatility on China's stock markets. The empirically observed probability distributions of log-returns are almost symmetric, highly leptokurtic, and characterized by a non-Gaussian profile for small index changes. Thus, the China's stock markets cannot be described by a random walk. We suggest that the correlation dynamics and stochastic changes of stock prices of China's stock markets are investigated by the Lorentz stable distribution. Features of stock price transiting from Y(t) to Y(t+?t) for small time interval is presented by transition distribution. We give an explicit expression of the transition probability distribution for the China's stock price changes. Another successful model is the truncated Levy flight. It is shown that both the stable Lorentz and truncated Levy flight distribution are in agreement with empirical observations on China's stock markets. As a comparison, we also discuss the properties of probability distribution of returns for USA' stock markets. It is found that, in spite of immature and a segmented market with domestic investors dominating ownership of stocks, China's stock markets possess the same distribution of returns with other financial markets in the world.
JEL classification numbers: G15, G17, C46
Keywords: China's stock markets, Stochastic volatility, stable Lorentz distribution, transition probability distribution