Signature-based identification of volatility models from path geometry — explained | StockTools Quant Research

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Signature-based identification of volatility models from path geometry

Òscar Burés, Rafael De Santiago · 2026-07-07

what this means for investors // AI summary of the abstractNiche / specialist

The authors turn observed volatility paths into geometric features (truncated path signatures) and feed them into a gradient boosting classifier to identify which class of stochastic volatility model produced the data, without fitting model parameters. In simulations, this distinguishes between structurally different models and even rough volatility models with close Hurst parameters, and it holds up when parameters are randomly varied. They find the first four signature levels carry most of the discriminative information.

Why it matters: For quants who model volatility, this suggests a data-driven way to decide which volatility model family best matches observed dynamics before committing to a full parametric calibration. It could help diagnose whether markets exhibit rough volatility behavior, though the work is entirely on simulated data.

Path signatures plus a gradient boosting classifier can distinguish stochastic volatility model classes without parametric calibration.
The method reportedly separates even rough volatility models with closely spaced Hurst parameters and works under parameter uncertainty.
Most discriminative information sits in the first four signature levels; higher orders add little.
Heston vs Ornstein-Uhlenbeck confusion is tied to the volatility-of-volatility parameter.

Applies to: stochastic volatility model selection and diagnostics

⚠ Results are from simulated paths only, so real-market performance with noisy, discretely observed data remains untested.

ABSTRACT

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.

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AI summary generated from the paper’s public abstract via arXiv; it may miss nuance — read the source before relying on it. Thank you to arXiv for its open-access interoperability; StockTools is not affiliated with arXiv, and all rights remain with the authors. Educational only, not financial advice.