Limit Order Book dynamics and order size modelling using Compound Hawkes Process

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. •We propose a novel formulation of the Hawkes Process to maintain positive spread.•We augment the non-parametric methods proposed in Kirchner 2017 to work with slow decaying kernels and to be more stable.•We make use of calibrated distributions for sampling the order sizes of the events rather than assuming unit order-size.•We formulate the in-spread order arrivals as a function of the current spread — utilizing the well known fact that spreads are mean-reverting.•We perform a MI study on this simulator along with testing against several baselines and comparing against empirical data.