Accurate forecasting of stock price movements is crucial for optimizing trade execution and mitigating risk in automated trading environments, especially when leveraging Limit Order Book (LOB) data. However, developing predictive models from LOB data presents substantial challenges due to its inherent complexities and high-frequency nature. In this thesis, the application of the General Compound Hawkes Process (GCHP) is explored to predict price volatility. Within this framework, a Hawkes process is employed to estimate the times of price changes, and a Markovian model is utilized to determine their amplitudes. The price volatility is obtained through both numerical and analytical methodologies. The performance of the GCHP is assessed on a publicly available dataset, including five distinct stocks. To enhance accuracy, the number of states in the Markov chain is gradually increased, and the advantages of incorporating a higher-order Markov chain for refined volatility estimation are demonstrated.