This paper introduces a novel Compound Hawkes Process (CHP) for modeling Limit Order Book (LOB) dynamics, addressing the limitation of constant order sizes in traditional Hawkes models. The authors propose a 12-dimensional Hawkes process where each event type (limit, cancel, market orders) at six price levels around the best bid and ask has its own intensity and order size distribution. The order sizes are sampled from calibrated distributions that capture empirical spikes at round numbers. To ensure the bid-ask spread remains positive, in-spread order intensities are modulated by a power law function of the current spread-in-ticks. The model also incorporates time-of-day seasonality and allows for inhibitory cross-excitation kernels using an enhanced non-parametric calibration method.

The methodology is validated using Level 2 NASDAQ data for Apple Inc. The results show that the CHP model accurately replicates key empirical properties, including the concave market impact function, volatility clustering, and correlated order flow. The paper provides a detailed calibration procedure and compares the model against several baselines, demonstrating superior performance. This work contributes to quantitative finance by offering a transparent, mathematically descriptive LOB simulator that captures both event timing and order size dynamics, making it suitable for applications such as market impact analysis and high-frequency trading strategy backtesting.