Signature-Based Execution for Path-Dependent Statistical Arbitrage

Summary

The paper presents an optimal-execution framework for statistical arbitrage when predictive signals depend on the path of market data. It represents both the alpha signal and trading speed as linear functions of a truncated signature of a time-augmented market path, so execution can respond to realized signal history. The formulation accounts for temporary market impact, inventory, terminal liquidation, and approximate dollar neutrality.

A quadratic reduction result turns the constrained class of signature-based policies into a finite-dimensional concave quadratic optimization over policy coefficients. In synthetic tests using a mean-reverting log-spread model, the fitted policy has higher return on turnover than a conventional z-score threshold benchmark. A historical equity pairs-trading backtest also reports better accounting performance for the fitted policy. The supplied description does not give implementation details or establish how results generalize beyond these settings.

Key ideas

• Signature features provide a common representation for path-dependent alpha and execution speed.
• The execution objective includes market impact, inventory exposure, liquidation, and approximate dollar neutrality.
• The restricted policy optimization reduces to a finite-dimensional concave quadratic programme.
• Synthetic and historical pairs-trading experiments report improvements over a z-score threshold benchmark.

Tags

# Signature-Based Optimal Execution for Statistical Arbitrage with Path-Dependent Trading Signals


# Signature-Based Optimal Execution for Statistical Arbitrage with Path-Dependent Trading Signals









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 classical $z$-score threshold benchmark. We show 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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

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