Tradable Itô Signatures: A Model-Free, Interpretable Framework for Dynamic Hedging

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Directly addresses dynamic hedging of derivatives, a core problem in quantitative trading and risk management. The framework is model-free, interpretable, computationally efficient, and validated on real S&P 500 options data. It provides a practical alternative to both classical Black-Scholes delta hedging and black-box neural network hedging. The tradability theorem ensures all hedging strategies are implementable with standard instruments. Particularly relevant for path-dependent exotic derivatives where classical methods fail.

The core framework involves: (1) computing discretized Itô signature coordinates (recursive, straightforward), (2) fitting a linear regression (OLS or Lasso) on signature features, and (3) assembling the hedge from basis strategies. The signature computation grows combinatorially with truncation order and dimension. The Lasso fitting is standard. The signature-kernel weighting adds complexity for computing path similarities. Overall, the method is described as 'computationally efficient, easy to implement' and runs in seconds vs. hours for neural networks. Key challenges: choosing truncation order, handling high-dimensional signature features, and computing signature kernels for weighting.

The paper provides detailed simulation setup (GBM parameters, training sizes, random seeds), computational environment specifications (hardware, software versions), and empirical data source (OptionMetrics S&P 500 Weekly options 2011-2025). All proofs are included in Appendix E. However, OptionMetrics data requires a commercial subscription. The signature computation and Lasso fitting procedures are described in detail. No GitHub repository is explicitly provided.