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 assets within this framework. We compute several statistical quantities and the covariance matrix associated with the diffusive limit of the model so that the relation between the parameters driving the assets at high and low frequencies is explicit. We illustrate the results using several financial assets quoted in the Eurex market and show how the model captures the lead–lag relationship between them. © 2016 Wiley Periodicals, Inc. Jrl Fut Mark 37:260–285, 2017