A Stock Market Model with Chartists, Fundamentalists, and Index Traders: Nonlinearities and Coexisting Attractors

In this paper, we develop a model, where the price dynamics of two stock markets are determined by the orders of chartists, fundamentalists, and index traders. Chartists bet on the persistence of bull and bear markets, while fundamentalists believe in mean reversion. The trading activity of index traders, who also rely on technical and fundamental analysis, links the price dynamics of the two stock markets. The models’ behavior is governed by a two-dimensional map featuring multiple nonlinearities. Using a combination of analytical and numerical tools, we demonstrate that the model can produce a surprisingly large number of coexisting attractors with intricate basins of attraction. Some attractors result in the comovement of stock prices, while others lead to countercyclical dynamics. Under the influence of exogenous noise, stock prices alternate between these attractors, displaying synchronous, independent, and asynchronous patterns, and fluctuating around different price levels. Importantly, however, such dynamics may also emerge in our deterministic model.