Modelling High-Frequency Data with Bivariate Hawkes Processes: Power-Law vs. Exponential Kernels

Paper: arXiv 2503.14814

Authors: Neal Batra

Abstract

This study explores the application of Hawkes processes to model high-frequency data in the context of limit order books. Two distinct Hawkes-based models are proposed and analyzed: one utilizing exponential kernels and the other employing power-law kernels. These models are implemented within a bivariate framework. The performance of each model is evaluated using high-frequency trading data, with a focus on their ability to reproduce key statistical properties of limit order books. Through a comprehensive comparison, we identify the strengths and limitations of each kernel type, providing insights into their suitability for modeling high-frequency financial data. Simulations are conducted to validate the models, and the results are interpreted. Based on these insights, a trading strategy is formulated.

Complexity vs Empirical Score

• Math Complexity: 5.0/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides standard definitions and formulas for bivariate Hawkes processes, but the empirical evaluation is severely limited as it relies on only a 2-second data sample of two stocks. It lacks statistical significance tests, detailed calibration validation, and an explicit trading strategy backtest.

Research Flowchart

  flowchart TD
    A[Research Goal: Model Limit Order Books via Bivariate Hawkes Processes] --> B[Input Data: High-Frequency Equity Trading Data]
    B --> C[Model Formulation: Compare Exponential vs. Power-Law Kernels]
    C --> D[Model Calibration & Simulation Processes]
    D --> E[Outcome 1: Evaluate Fit to LOB Statistical Properties]
    D --> F[Outcome 2: Formulate & Validate Trading Strategy]