Hedging with memory: shallow and deep learning with signatures

ArXiv ID: 2508.02759 “View on arXiv”

Authors: Eduardo Abi Jaber, Louis-Amand Gérard

Abstract

We investigate the use of path signatures in a machine learning context for hedging exotic derivatives under non-Markovian stochastic volatility models. In a deep learning setting, we use signatures as features in feedforward neural networks and show that they outperform LSTMs in most cases, with orders of magnitude less training compute. In a shallow learning setting, we compare two regression approaches: the first directly learns the hedging strategy from the expected signature of the price process; the second models the dynamics of volatility using a signature volatility model, calibrated on the expected signature of the volatility. Solving the hedging problem in the calibrated signature volatility model yields more accurate and stable results across different payoffs and volatility dynamics.

Keywords: Hedging, Path Signatures, Non-Markovian Stochastic Volatility, Neural Networks, LSTMs

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rats
• Why: The paper is mathematically dense, involving advanced concepts from tensor algebra and stochastic calculus to define path signatures, and includes theoretical proofs like universal approximation theorems. However, it primarily presents a methodology and comparative analysis without providing code, detailed backtesting metrics, or specific dataset results, focusing more on theoretical and algorithmic contributions.

  flowchart TD
    A["Research Goal:<br>Hedging exotic derivatives<br>under non-Markovian<br>stochastic volatility"] --> B["Input Data:<br>Simulated price paths<br>with complex volatility dynamics"]
    B --> C["Deep Learning:<br>Signatures as features<br>in Feedforward Neural Networks"]
    B --> D["Shallow Learning:<br>Signature Volatility Model<br>+ Regression Strategies"]
    C --> E["Compare with<br>LSTM baseline"]
    D --> F["Calibration:<br>Match expected signatures<br>of volatility process"]
    C & E & F --> G["Key Findings:<br>Signatures outperform LSTMs<br>with less compute.<br>Signature models yield<br>more stable hedging strategies."]