High-Frequency Market Manipulation Detection with a Markov-modulated Hawkes process

ArXiv ID: 2502.04027 “View on arXiv”

Authors: Unknown

Abstract

This work focuses on a self-exciting point process defined by a Hawkes-like intensity and a switching mechanism based on a hidden Markov chain. Previous works in such a setting assume constant intensities between consecutive events. We extend the model to general Hawkes excitation kernels that are piecewise constant between events. We develop an expectation-maximization algorithm for the statistical inference of the Hawkes intensities parameters as well as the state transition probabilities. The numerical convergence of the estimators is extensively tested on simulated data. Using high-frequency cryptocurrency data on a top centralized exchange, we apply the model to the detection of anomalous bursts of trades. We benchmark the goodness-of-fit of the model with the Markov-modulated Poisson process and demonstrate the relevance of the model in detecting suspicious activities.

Keywords: Point Processes, Hawkes Process, Hidden Markov Model, High-Frequency Trading, Anomaly Detection

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.5/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematics, including a Markov-modulated Hawkes process, expectation-maximization algorithms, and ODE solutions, scoring high in math complexity. It also demonstrates empirical rigor by validating estimators on simulations and applying the model to real high-frequency cryptocurrency data for detection of suspicious trading activities.

  flowchart TD
    A["Research Goal:<br>High-Frequency Market Manipulation Detection"] --> B["Methodology:<br>Markov-modulated Hawkes Process<br>Hawkes excitation kernels"]

    subgraph Inputs
        direction LR
        B1["Simulated Data<br>for Convergence Tests"] --> C
        B2["High-Frequency Crypto Data<br>Trade Events"] --> C
    end

    B --> C["Statistical Inference:<br>Expectation-Maximization Algorithm"]

    C --> D["Computational Process:<br>Estimation of Parameters<br>Intensities & Transition Probabilities"]

    D --> E{"Benchmarking<br>vs. Markov-modulated Poisson"}

    E --> F["Key Findings:<br>1. Convergence validated on simulation<br>2. Superior Goodness-of-Fit<br>3. Detection of anomalous trade bursts"]