This paper models stochastic process of price time series of $CSI$ $300$ index in Chinese financial market, analyzes volatility characteristics of intraday high-frequency price data. In the new generalized Barndorff-Nielsen and Shephard model, the lag caused by asynchrony of market information and market microstructure noises are considered, and the problem of lack of long-term dependence is solved. To speed up the valuation process, several machine learning and deep learning algorithms are used to estimate parameter and evaluate forecast results. Tracking historical jumps of different magnitudes offers promising avenues for simulating dynamic price processes and predicting future jumps. Numerical results show that the deterministic component of stochastic volatility processes would always be captured over short and longer-term windows. Research finding could be suitable for influence investors and regulators interested in predicting market dynamics based on high-frequency realized volatility.