Correlation and Lead-Lag Relationships in a Hawkes Microstructure Model

The aim of this paper is to develop a multi-asset model based on the Hawkes process describing the evolution of assets at high frequency and to study the lead-lag relationship as well as the correlation between the stocks within this framework. Thanks to its strong analytical tractability several statistical quantities are explicitly computed and give some insight on the impact of the model parameters on these quantities. Furthermore, we compute the covariance matrix associated with the diffusive limit of the model so that the relation between the parameters driving the asset at high and low frequencies is explicit. We illustrate our results using index futures and stocks quoted in the Eurex market. The model can capture the existing lead-lag relationship between the assets