A Deterministic Limit Order Book Simulator with Hawkes-Driven Order Flow
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
Cite
@article{arxiv.2510.08085,
title = {A Deterministic Limit Order Book Simulator with Hawkes-Driven Order Flow},
author = {Sohaib El Karmi},
journal= {arXiv preprint arXiv:2510.08085},
year = {2025}
}
Comments
22 pages, 7 figures, includes theoretical proofs, simulator architecture, and calibration results. Code available at https://github.com/sohaibelkarmi/High-Frequency-Trading-Simulator