High frequency trading activity is not memoryless process, and trades also tend to cluster, thus justifying the use of the Hawkes process for modelling framework. In this talk, I shall review some existing stochastic models for the dynamic of a limit order books (LOB) based on point processes. Then I shall introduce new various stochastic models for the dynamic of an asset mid-price (the mean of the best ask and the best bid prices) in LOB based on so-called general compound Hawkes process: the number of price changes up to time t and the consecutive price increments are described by the Hawkes process N(t) and a Markov chain, respectively, and, as a result, the mid-price is the random sum of price increments on the interval [0, t]. The diffusive limits for the latter asset models will be computed, connecting the parameters driving the high-frequency activities to the daily volatilities, and thus making the explicit link between the microscopic activity and the macroscopic one. This approach will be justified and illustrated by calibrating those models to the real market datasets. Finally, I shall present some ideas on stochastic modelling for the mid-prices of multivariate assets based on our approach.