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被用于多种方式建模限价订单簿（LOB）动态，然而研究重点局限于捕捉事件间时间间隔，订单规模通常被假定为常量。我们提出了一种创新方法，利用复合霍克斯过程对LOB进行建模，其中每个事件对应的订单规模从校准后的分布中采样。该过程以新颖方式构建，确保过程价差始终保持正值。此外，我们将模型参数根据交易时段进行条件化处理，以契合实证观察结果。我们采用增强型非参数方法对霍克斯核函数进行校准，并允许存在抑制性交叉激励核函数。我们展示了纳斯达克交易所某权益股票LOB的拟合结果与质量，并将其与多个基线方法进行对比。最后，我们基于该模拟器开展了市场冲击研究，结果显示凹形市场冲击函数的实证观察确实得以复现。