Opinion Formation Model on Random Graphs for Financial Markets

We investigate the financial market dynamics by proposing a heterogeneous agent-based opinion formation model. In this work, we classify the individuals in a financial market by their trader strategy, namely noise traders and fundamentalists. The local majority drives the market exchanging behavior of noise traders, whereas the global minority of the network influences the fundamentalist agents. We represent the individuals as nodes in an Erdös-Rényi random graph and, at a given time, they assume one of two opinion states, +1 or -1, regarding buying or selling an asset. Our model presents such fundamental qualitative and quantitative real-world market features as the distribution of logarithmic returns with fat-tails, clustered volatility, and long-term correlation of returns. We use Student's t distributions to fit the histograms of logarithmic returns, showing the gradual shift from a leptokurtic to a mesokurtic regime, depending on the fraction of fundamentalist agents. We also investigate the distribution of logarithmic returns of several real-world financial indices.