  We introduce and treat rigorously a new multi-agent model of the continuous
double auction or in other words the order book (OB). It is designed to explain
collective behaviour of the market when new information affecting the market
arrives. The novel feature of the model is two additional slow changing
parameters, the so-called sentiment functions. These sentiment functions
measure the conception of the fair price of two groups of investors, namely,
bulls and bears. Our model specifies differential equations for the time
evolution of sentiment functions and constitutes a nonlinear Markov process
which exhibits long term correlations. We explain the intuition behind
equations for sentiment functions and present numerical simulations which show
that the behaviour of our model is similar to the behaviour of the real market.
We also obtain a diffusion limit of the model, the Ornstein-Uhlenbeck type
process with variable volatility. The volatility is proportional to the
difference of opinions of bulls and bears about the fair price of a security.
The paper is complimentary to our previous work where mathematical proofs are
presented.
