Before revision:  We take the exchange to be an order-driven market and propose a continuous-time setup for the best bid price and the market spread, both modelled by functions of the market activity. We consider a random drift so to include the impact of market orders, and we describe the arrival of limit orders and of order cancellations by means of Poisson random measures.
After revision:  We take the exchange to be an order-driven market and propose a continuous-time setup for the best bid price and the market spread, both modelled by Levy processes.