| Abstract: |
Simulations of agent-based models have shown that the stylized facts
(unit-root, fat tails and volatility clustering) of financial markets have a
possible explanation in the interactions among agents. However, the
complexity, originating from the presence of non-linearity and interactions,
often limits the analytical approach to the dynamics of these models. In this
paper we show that even a very simple model of a financial market with
heterogeneous interacting agents is capable of reproducing realistic
statistical properties of returns, in close quantitative accordance with the
empirical analysis. The simplicity of the system also permits some analytical
insights using concepts from statistical mechanics and physics. In our model,
the traders are divided into two groups : fundamentalists and chartists, and
their interactions are based on a variant of the herding mechanism introduced
by Kirman [22]. The statistical analysis of our simulated data shows long-term
dependence in the auto-correlations of squared and absolute returns and
hyperbolic decay in the tail of the distribution of the raw returns, both with
estimated decay parameters in the same range like empirical data. Theoretical
analysis, however, excludes the possibility of ’true’ scaling behavior because
of the Markovian nature of the underlying process and the finite set of
possible realized returns. The model, therefore, only mimics power law
behavior. Similarly as with the phenomenological volatility models analyzed in
LeBaron [25], the usual statistical tests are not able to distinguish between
true or pseudo-scaling laws in the dynamics of our artificial market. |