Nonparametric Estimation of Self- and Cross-Impact

Battle Count: 77

This paper is directly and highly relevant to quantitative trading. It provides a practical, data-driven framework for estimating market impact (both self- and cross-impact) without parametric assumptions, which is critical for optimal execution, trading cost estimation, and portfolio management. The nonparametric approach avoids parameter explosion in multi-asset settings (a major practical challenge for institutional traders). The empirical findings on concavity (square-root law extending to cross-impact), asymmetric cross-impact driven by liquidity differences, and power-law decay are directly actionable for trading strategy design. The use of both proprietary metaorder data and public order flow data demonstrates broad applicability.

The core estimation involves solving a regularized least-squares problem (closed-form via matrix inversion) followed by a convex projection onto the admissible kernel set (solvable via standard convex optimization packages like CVXPY). The main complexity lies in: (1) constructing the design matrices U^(n) for multi-asset settings, (2) the synthetic metaorder proxy generation requiring careful parameter calibration, (3) proper normalization for intraday volatility and volume patterns, (4) handling the tensor structure of multi-asset kernels (M×d×d), and (5) the grid search for parametric model comparison. The nonparametric estimator itself requires zero tuned parameters, simplifying deployment.

The methodology is fully described with mathematical proofs and algorithmic details. However, the primary dataset (CFM proprietary metaorder data) is not publicly available. The public S&P 500 order flow data from LOBSTER is accessible but requires a subscription. The synthetic metaorder proxy construction algorithm is described in detail. Theoretical results (Theorems 2.4 and 2.10) are fully proven in the appendix. No code repository is mentioned.