Investor's sentiment in multi-agent model of the continuous double auction

Abstract: 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.