Аннотация: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
behavior 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 behavior of our model is similar to the behavior 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.