Hawkes Process Models for High-Frequency Trade Arrivals

We study multivariate Hawkes processes as models for high-frequency trade arrivals, capturing the self-exciting and cross-exciting structure of order flow across asset classes. The intensity of each arrival stream depends on the full history of all streams via a matrix of exponential kernels, whose parameters are estimated by maximum likelihood using an expectation-maximisation algorithm. Calibrated on simulated tick data, the model reproduces the clustering of trades, the elevated autocorrelation of inter-arrival times, and the asymmetric cross-excitation patterns characteristic of correlated liquid assets.