This thesis investigates the use of Neural Ordinary and Stochastic Differential Equations (Neural ODEs and Neural SDEs) for modelling the continuous-time evolution of investor sentiment and its impact on financial markets. The work begins by collecting sentiment data from financial news sources, which inherently exhibit irregular sampling and stochastic variability. Sentiment scores—derived using LLM models such as GPT-4.0 —are treated as time-dependent signals representing collective market mood. Neural ODEs are then employed to learn smooth latent trajectories that capture the underlying dynamics of these sentiment processes, while Neural SDEs extend this approach to model uncertainty and volatility in sentiment evolution. The learned latent representations are subsequently integrated into downstream forecasting models, including Neural SDE-based predictors, to assess their contribution to stock price and return prediction. Comparative analyses are conducted against conventional discrete-time and feature-based baselines to quantify the benefits of continuous-time modelling. Overall, this research aims to determine whether modelling sentiment as a continuous stochastic process enhances the interpretability and predictive performance of financial time series models.