  We propose a new model for the level I of a Limit Order Book (LOB), which
incorporates the information about the standing orders at the opposite side of
the book after each price change and the arrivals of new orders within the
spread. Our main result gives a diffusion approximation for the mid-price
process. To illustrate the applicability of the considered framework, we also
propose a feasible method to compute several quantities of interest}, such as
the distribution of the time span between price changes and the probability of
consecutive price increments conditioned on the current state of the book. The
proposed method is used to develop an efficient simulation scheme for the price
dynamics, which is then applied to assess numerically the accuracy of the
diffusion approximation.
