Trade Execution Flow as the Underlying Source of Market Dynamics

ArXiv ID: 2511.01471 “View on arXiv”

Authors: Mikhail Gennadievich Belov, Victor Victorovich Dubov, Vadim Konstantinovich Ivanov, Alexander Yurievich Maslov, Olga Vladimirovna Proshina, Vladislav Gennadievich Malyshkin

Abstract

In this work, we demonstrate experimentally that the execution flow, $I = dV/dt$, is the fundamental driving force of market dynamics. We develop a numerical framework to calculate execution flow from sampled moments using the Radon-Nikodym derivative. A notable feature of this approach is its ability to automatically determine thresholds that can serve as actionable triggers. The technique also determines the characteristic time scale directly from the corresponding eigenproblem. The methodology has been validated on actual market data to support these findings. Additionally, we introduce a framework based on the Christoffel function spectrum, which is invariant under arbitrary non-degenerate linear transformations of input attributes and offers an alternative to traditional principal component analysis (PCA), which is limited to unitary invariance.

Keywords: execution flow, market dynamics, Radon-Nikodym derivative, Christoffel function, market microstructure

Complexity vs Empirical Score

• Math Complexity: 9.0/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematics, including Radon-Nikodym derivatives, eigenproblems, and Christoffel function spectra, indicating high complexity. It is validated on actual high-frequency market data with a computational framework and software release, demonstrating strong empirical rigor.

  flowchart TD
    A["Research Goal<br>Identify Fundamental Driver of Market Dynamics"] --> B["Methodology: Numerical Framework"]
    B --> C{"Input: Sampled Market Moments"}
    C --> D["Compute Execution Flow I = dV/dt<br>via Radon-Nikodym Derivative"]
    D --> E["Christoffel Function Spectrum<br>Invariant to Linear Transformations"]
    E --> F["Derive Characteristic Time Scale<br>Solve Eigenproblem"]
    F --> G["Validation on Market Data"]
    G --> H["Key Outcomes<br>Execution Flow is Fundamental Driver<br>Actionable Triggers Identified<br>Alternative to PCA"]