  A simple Hawkes model have been developed for the price tick structure
dynamics incorporating market microstructure noise and trade clustering. In
this paper, the model is extended with random mark to deal with more realistic
price tick structures of equities. We examine the impact of jump in price
dynamics to the future movements and dependency between the jump sizes and
ground intensities. We also derive the volatility formula based on stochastic
and statistical methods and compare with realized volatility in simulation and
empirical studies. The marked Hawkes model is useful to estimate the intraday
volatility similarly in the case of simple Hawkes model.
