Hawkes Process has been used to model Limit Order Book (LOB) dynamics in several ways in the literature however the focus has been limited to capturing the inter-event times while the order size is usually assumed to be constant. We propose a novel methodology of using Compound Hawkes Process for the LOB where each event has an order size sampled from a calibrated distribution. The process is formulated in a novel way such that the spread of the process always remains positive. Further, we condition the model parameters on time of day to support empirical observations. We make use of an enhanced non-parametric method to calibrate the Hawkes kernels and allow for inhibitory cross-excitation kernels. We showcase the results and quality of fits for an equity stock's LOB in the NASDAQ exchange and compare them against several baselines. Finally, we conduct a market impact study of the simulator and show the empirical observation of a concave market impact function is indeed replicated.

翻译：霍克斯过程在文献中已多次用于建模限价订单簿动态，但研究重点局限于捕获事件间时间间隔，而订单规模通常被假设为常量。我们提出一种新颖方法，利用复合霍克斯过程对限价订单簿进行建模，其中每个事件对应的订单规模从已校准的分布中采样。该过程以创新方式构建，确保价差始终为正值。此外，我们将模型参数与日内时间条件关联以符合实证观测结果。通过增强型非参数方法校准霍克斯核函数，并允许抑制性交叉激励核函数的存在。我们在纳斯达克交易所某权益股票的限价订单簿上展示了模型结果与拟合质量，并将其与多个基准模型进行对比。最后，我们开展模拟器的市场冲击研究，证实凹形市场冲击函数这一实证观测结果确实得以复现。