A Deterministic Limit Order Book Simulator with Hawkes-Driven Order Flow

ArXiv ID: 2510.08085 “View on arXiv”

Authors: Sohaib El Karmi

Abstract

We present a reproducible research framework for market microstructure combining a deterministic C++ limit order book (LOB) simulator with stochastic order flow generated by multivariate marked Hawkes processes. The paper derives full stability and ergodicity proofs for both linear and nonlinear Hawkes models, implements time-rescaling and goodness-of-fit diagnostics, and calibrates exponential and power-law kernels on Binance BTCUSDT and LOBSTER AAPL datasets. Empirical results highlight the nearly-unstable subcritical regime as essential for reproducing realistic clustering in order flow. All code, datasets, and configuration files are publicly available at https://github.com/sohaibelkarmi/High-Frequency-Trading-Simulator

Keywords: Hawkes Processes, Limit Order Book (LOB), High-Frequency Trading, Market Microstructure, Simulation, Equities

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail
• Why: The paper is mathematically dense, deriving full stability and ergodicity proofs for Hawkes processes with extensive LaTeX notation, while also demonstrating high empirical rigor through a reproducible C++ simulator, calibration on real LOBSTER and Binance datasets, and statistical diagnostics.

  flowchart TD
    G["Research Goal:<br/>Reproducible LOB Simulator with<br/>Hawkes-Driven Order Flow"] --> D["Data Inputs:<br/>Binance BTCUSDT & LOBSTER AAPL<br/>(High-Frequency)"]
    D --> M["Methodology:<br/>Multivariate Marked Hawkes<br/>(Linear & Nonlinear)"]
    M --> C["Computational Process:<br/>Deterministic C++ LOB<br/>& Stochastic Order Flow"]
    C --> F["Key Findings & Outcomes:<br/>Stability Proofs, Empirical Calibration,<br/>Subcritical Regime, Public Code"]