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以多种方式用于建模限价订单簿动态，然而其焦点通常局限于捕捉事件间时间间隔，而订单规模通常被假定为常数。我们提出一种新颖的方法，将复合霍克斯过程应用于限价订单簿建模，其中每个事件的订单规模均从校准后的分布中采样。该过程以一种新颖方式构建，确保过程的买卖价差始终保持为正。此外，我们将模型参数与日内时间相关联以支持实证观察。我们采用一种增强的非参数方法来校准霍克斯核函数，并允许抑制性交叉激励核的存在。我们展示了纳斯达克交易所某股票限价订单簿的拟合结果与质量，并与多种基线模型进行了比较。最后，我们对模拟器进行了市场冲击研究，结果表明实证观察到的凹型市场冲击函数确实得到了复现。