🤖 AI Summary
This study addresses the optimal execution problem in statistical arbitrage under path-dependent trading signals, incorporating temporary market impact, inventory risk, terminal liquidation, and an approximate dollar-neutrality constraint. The work innovatively models both the alpha signal and trading speed as linear functionals of time-augmented, path-truncated signatures, thereby unifying signal generation and execution within a single framework. A quadratic reduction theorem is introduced, transforming the original infinite-dimensional path-dependent optimization into a finite-dimensional concave quadratic program, which enables efficient computation of optimal strategy coefficients. Backtesting on historical stock pairs using a mean-reverting log-spread model demonstrates that the proposed strategy significantly outperforms the conventional z-score threshold benchmark in terms of turnover-adjusted returns.
📝 Abstract
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.