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Gianmarco Morbelli, Sven Karbach, Mike Derksen · 2026-06-30
The paper builds a math framework using 'path signatures' to decide both when a trading signal fires and how fast to trade in statistical arbitrage (pairs-type) strategies. Its key result is that, within their chosen class of trading rules, the execution problem simplifies to a solvable finite-dimensional quadratic optimization that accounts for market impact, inventory, final liquidation, and rough dollar neutrality. In synthetic tests and one historical equity pairs backtest, the fitted policy beat a standard z-score threshold rule on return-per-turnover.
Why it matters: Practitioners running pairs or stat-arb strategies might find value in tying signal generation and execution together rather than treating them separately, potentially improving return relative to trading activity. The signature approach offers a structured, tractable way to make execution respond to the full recent history of a signal instead of a single threshold.
⚠ Evidence is limited to synthetic experiments and a single historical pairs backtest measured in accounting terms, so live-trading robustness and generalization are unproven.
We develop a signature-based framework for optimal execution in statistical arbitrage strategies with path-dependent predictive signals. Both the alpha process and the trading speed are modelled as linear functionals of the truncated signature of a time-augmented market path, placing signal generation and execution on the same truncated signature basis. This allows the trading rule to react to the realised history of the signal while accounting for temporary impact, inventory exposure, terminal liquidation, and approximate dollar neutrality The main contribution is a quadratic reduction theorem: within the class of signature-linear trading speeds, the restricted path-dependent execution problem becomes a finite-dimensional concave quadratic programme in the policy coefficients. After running synthetic experiments under a mean-reverting log-spread model, we find that the fitted policy achieves a higher return on turnover than a z-score classical threshold benchmark. We shows how the same workflow can be deployed on a historical equity pairs-trading backtest, where the fitted signature policy again outperforms the benchmark in accounting terms.
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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.