  We propose a three-state microscopic opinion formation model for the purpose
of simulating the dynamics of financial markets. In order to mimic the
heterogeneous composition of the mass of investors in a market, the agent-based
model considers two different types of traders: noise traders and contrarians.
Agents are represented as nodes in a network of interactions and they can
assume any of three distinct possible states (e.g. buy, sell or remain
inactive). The time evolution of the state of an agent is dictated by
probabilistic dynamics that include both local and global influences. A noise
trader is subject to local interactions, tending to assume the majority state
of its nearest neighbors, whilst a contrarian is subject to a global
interaction with the behavior of the market as a whole, tending to assume the
state of the global minority of the market. The model exhibits the typical
qualitative and quantitative features of real financial time series, including
distributions of returns with heavy tails, volatility clustering and long-time
memory for the absolute values of the returns. The distributions of returns are
fitted by means of coupled Gaussian distributions, quantitatively revealing
transitions between leptokurtic, mesokurtic and platykurtic regimes in terms of
a non-linear statistical coupling which describes the complexity of the system.
