  Following a long tradition of physicists who have noticed that the Ising
model provides a general background to build realistic models of social
interactions, we study a model of financial price dynamics resulting from the
collective aggregate decisions of agents. This model incorporates imitation,
the impact of external news and private information. It has the structure of a
dynamical Ising model in which agents have two opinions (buy or sell) with
coupling coefficients which evolve in time with a memory of how past news have
explained realized market returns. We study two versions of the model, which
differ on how the agents interpret the predictive power of news. We show that
the stylized facts of financial markets are reproduced only when agents are
over-confident and mis-attribute the success of news to predict return to
herding effects, thereby providing positive feedbacks leading to the model
functioning close to the critical point. Our model exhibits a rich multifractal
structure characterized by a continuous spectrum of exponents of the power law
relaxation of endogenous bursts of volatility, in good agreement with previous
analytical predictions obtained with the multifractal random walk model and
with empirical facts.
