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

Battle Count: 76

Directly addresses the core problem of how to execute statistical arbitrage signals optimally in liquid markets. The framework unifies signal generation and execution in one tractable model, provides explicit closed-form solutions, and demonstrates practical outperformance over classical z-score benchmarks. The signature-based approach captures path-dependent information (Lévy area, lead-lag, time ordering) that classical Markovian execution models miss. Highly relevant for execution desks, quant researchers in statistical arbitrage, and algorithmic trading practitioners. The operational message (expensive calibration offline, simple matrix multiply live) is directly actionable.

The theoretical framework requires understanding of rough path signatures, tensor algebra, and Kronecker products. However, the actual implementation is relatively straightforward: (1) compute truncated signature features from market data, (2) assemble empirical moment matrices A and b from training paths, (3) solve a single regularized linear system theta* = -1/2(A-rho*I)^{-1}b, (4) at live execution, compute current signature vector x_t and apply v_t = B*x_t. The main complexity lies in correctly computing signature features (especially at level 2+) and assembling the Kronecker-product tensor blocks. The paper provides detailed formulas and validation checks. No specialized ML training or iterative optimization is needed.

The paper provides complete mathematical derivations, explicit formulas for all matrices (A, b, c), detailed parameter settings for both synthetic and historical experiments, and comprehensive appendices with tensor expansions, shuffle-algebra formulations, and closed-form OU moment calculations. The synthetic data-generating process is fully specified. However, no code repository is mentioned, and the historical Shell-BP data would need to be sourced separately. The numerical validation (quadratic reduction check with 2.2e-7 max relative error) provides strong evidence of implementation correctness.