Heterogeneity and endogenous nonlinearity in an artificial stock model

Abstract

We present a nonlinear structural stock market model which is a nonlinear deterministic process buffeted by dynamic noise. The market is composed of two typical trader types, the rational fundamentalists believing that the price of an asset is determined solely by its fundamental value and the boundedly rational noise traders governed by greed and fear. The interaction among heterogeneous investors determines the dynamics and the statistical properties of the system. We find the model is able to generate time series that exhibit dynamical and statistical properties closely resembling those of the S&P500 index, such as volatility clustering, fat tails (leptokurtosis), autocorrelation in square and absolute return, larger amplitude, crashes and bubbles. We also investigate the nonlinear dependence structure in our data. The results indicate that the GARCH-type model cannot completely account for all nonlinearity in our simulated market, which is thus consistent with the results from real markets. It seems that the nonlinear structural model is more powerful to give a satisfied explanation to market behavior than the traditional stochastic approach. © 2008 Springer-Verlag Berlin Heidelberg.