Modeling Stock Price Dynamics with Fuzzy Opinion Networks

We propose a mathematical model for the word-of-mouth communications among stock investors through social networks and explore how the changes of the investors' social networks influence the stock price dynamics. First, we use a Gaussian fuzzy set to model the stock price expectation of an investor, where the center and the standard deviation of the Gaussian fuzzy set represent the expected price and the uncertainty about the expected price, respectively. Then, based on a similarity measure between Gaussian fuzzy sets, we propose a bounded confidence fuzzy opinion network (BCFON) to model the social connection of investors, where only those investors whose stock price expectations are close to each other are connected, and the investors in a connected group update their fuzzy expectations as weighted averages of the previous fuzzy expectations of their neighbors. Finally, the fuzzy expectations from the BCFON are used as inputs to drive the stock price dynamics. Simulations of the price dynamic models show the details of how the topological changes of the investor networks influence the moves of the stock prices, and some common phenomena in real stock prices, such as excess volatility and trend shifting, are observed in the simulated price series and can be easily explained in our model framework. We give rigorous mathematical proofs for the convergence properties of the BCFON