Paper: arXiv 2510.08085

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

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: 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.

Research Flowchart

  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"]

Cited References (18)

  1. Spectra of Some Self‐Exciting and Mutually Exciting Point Processes (1971) — link
  2. A Cluster Process Representation of a Self‐Exciting Process (1974) — link
  3. Stability of Nonlinear Hawkes Processes (1996) — link
  4. Simulation of Nonhomogeneous Poisson Processes by Thinning (1979) — link
  5. Artifact Review and Badging Policy (2020)
  6. Binance REST API for Market and Order Book Data (2025)
  7. On Lewis’ Simulation Method for Point Processes (1981) — link
  8. Statistical Models for Earthquake Occurrences and Residual Analysis for Point Processes (1988) — link
and 10 more
  1. The Time‐Rescaling Theorem and Its Application to Neural Spike Train Data Analysis (2002) — link
  2. An Introduction to the Theory of Point Processes, Vol. II: General Theory and Structure (2008)
  3. Limit Theorems for Nearly Unstable Hawkes Processes (2015) — link
  4. Hawkes Processes in Finance (2015) — link
  5. Second‐Order Statistics Characterization of Hawkes Processes and Non‐Parametric Estimation (2016) — link
  6. Price Dynamics in a Markovian Limit Order Market (2013) — link
  7. Simulating and Analyzing Order Book Data: The Queue-Reactive Model (2015) — link
  8. LOBSTER: Limit Order Book Reconstruction System (2011) — link
  9. Modelling Security Market Events in Continuous Time: Intensity Based, Multivariate Point Process Models (2007) — link
  10. The Fourth Industrial Revolution (2016) — link

0 of 18 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.