Signature-based identification of volatility models from path geometry
We propose a signature-based framework for the identification of stochastic volatility model classes from observed path data. By mapping volatility trajectories into a feature space via truncated path signatures and applying a gradient boosting classifier, we show that it is possible to distinguish between different classes of volatility dynamics without relying on parametric calibration. Through a series of numerical experiments, we demonstrate that the method achieves high classification accuracy across a range of settings, from structurally distinct models to cases involving rough volatility models with closely spaced Hurst parameters. We show that the method remains effective under parameter uncertainty, where each simulated path is drawn with randomly sampled model parameters, and provide a detailed analysis of the misclassification pattern between the Heston and Ornstein--Uhlenbeck models in terms of the volatility of volatility parameter. The results highlight that most of the relevant discriminative information is captured by the first four levels of the signature, while higher-order terms provide only marginal improvements. Overall, the findings support the view that stochastic volatility models can be effectively identified through the geometry of their sample paths.