🤖 AI Summary
This work addresses key limitations of Hawkes processes in market microstructure modeling—namely, instability, calibration difficulty, and irreproducible simulation. We propose a reproducible research framework integrating a deterministic C++ limit-order-book (LOB) simulator with a multivariate marked Hawkes process. Methodologically, we provide the first rigorous theoretical proofs of stability and ergodicity for both linear and nonlinear Hawkes models, revealing the critical role of the subcritical regime in capturing order-flow clustering. Calibration employs an exponential–power-law hybrid kernel, combined with time-rescaling and goodness-of-fit diagnostics for precision. Our framework successfully reproduces temporal clustering characteristics of real order flows on Binance BTC/USDT and LOBSTER AAPL datasets. All code, data, and configuration files are publicly released, enabling fully reproducible high-frequency market dynamics research.
📝 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