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.

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动态，然而现有研究主要局限于捕获事件间隔时间，而订单规模通常被假定为常数。我们提出了一种利用复合霍克斯过程建模限价订单簿的新方法，其中每个事件均从标定分布中采样对应的订单规模。该过程以创新方式构建，确保过程价差始终保持正值。此外，我们将模型参数与日内时间条件关联以支持实证观测。我们采用增强非参数方法标定霍克斯核，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建模结果与拟合质量。