Stock volatility as an anomalous diffusion process

# Anomalous diffusion stocks In financial markets, understanding asset volatility—whether historical or implied—is essential for investors. This paper presents a new approach for estimating the volatility of stocks or similar assets using principles of anomalous diffusion, applied through Recurrent Neural Networks (RNNs). We employ an innovative RNN architecture, combining convolutional layers with bidirectional LSTMs, in a model known as UPV-MAT (developed by Universitat Politècnica de València - Matemática Aplicada), which was initially created for the AnDi-challenge. The model calculates the diffusion exponent as a measure of volatility and classifies market movements into five distinct diffusion types: ATTM (Annealed Transit Time Model), CTRW (Continuous Time Random Walk), FBM (Fractional Brownian Motion), LW (Levy Walk), and SBM (Scaled Brownian Motion). Our findings suggest that the diffusion exponent derived from anomalous diffusion processes, as determined by the UPV-MAT model, provides a valuable tool for analyzing stock market volatility. This approach sheds light on whether a stock is experiencing sub-diffusion, super-diffusion, or normal diffusion, offering a more comprehensive view of market dynamics than traditional volatility metrics.