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：文献中已采用霍克斯过程以多种方式建模限价订单簿动态，但研究重点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，其中每个事件关联的订单规模从校准后的分布中采样。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契合实证观测结果。我们采用增强的非参数方法校准霍克斯核函数，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限价订单簿的拟合结果与质量。