Sentiment-Driven Stochastic Volatility: An Observable Second Factor from Market Attention

We introduce a two-factor stochastic volatility model in which the mean-reversion speed of a Cox–Ingersoll–Ross variance process is an observable functional of a market attention field rather than a latent factor. The field admits an exact Feynman–Kac representation and generates closed-form volatility forecasts. The model nests the Heston volatility model, provides measurement-stable dynamics under observable data aggregation, and preserves its structure under an equivalent martingale measure. A mean-field analysis establishes convergence of the underlying particle system, while simulations demonstrate volatility and option-pricing differences following attention shocks.