Tradable It\^o Signatures: A Model-Free, Interpretable Framework for Dynamic Hedging

We propose an interpretable machine-learning framework for dynamic hedging using the It\^o signature transform, which turns asset-price paths into a set of linear features that universally represent nonlinear functions on time-series. We show that each discretized It\^o signature component can be perfectly replicated by a simple self-financing strategy using only the underlying assets and cash, which turns It\^o signature components into tradable and transparent hedging bases. This allows nonlinear derivative payoffs to be approximated by linear combinations of signature terms and hedged through the corresponding combination of trading strategies. We further establish a new approximation result for the It\^o signature and derive theoretical bounds for both in-sample and out-of-sample hedging errors. Our method is computationally efficient, easy to implement, and avoids the estimation of future conditional expectations, which makes it attractive for real-world applications. In simulations, our method delivers strong sample efficiency at substantially lower computational cost than neural-network benchmarks. In an empirical study of S\&P 500 index options, it performs robustly across vanilla and path-dependent contracts, with the signature-kernel weighted version providing further gains by localizing estimation to similar historical market paths. Overall, the paper identifies the It\^o signature as a practical, transparent, and model-agnostic implementation framework for dynamic hedging.