Minimal Agent Based Model for Financial Markets II: Statistical Properties of the Linear and Multiplicative Dynamics

TL;DR

This paper analyzes a minimal agent-based model of financial markets, exploring its linear and nonlinear dynamics to understand the origin of Stylized Facts and their self-organization, highlighting how nonlinearities amplify fluctuations.

Contribution

It introduces a generalized nonlinear version of a minimal agent-based market model, providing analytical insights and comparing its properties to the linear case, emphasizing the role of nonlinear dynamics.

Findings

Nonlinear dynamics increase fluctuations and Stylized Facts evidence.

Linear approximation allows analytical interpretation of model dynamics.

Both models exhibit similar self-organization of Stylized Facts.

Abstract

We present a detailed study of the statistical properties of an Agent Based Model and of its generalization to the multiplicative dynamics. The aim of the model is to consider the minimal elements for the understanding of the origin of the Stylized Facts and their Self-Organization. The key elements are fundamentalist agents, chartist agents, herding dynamics and price behavior. The first two elements correspond to the competition between stability and instability tendencies in the market. The herding behavior governs the possibility of the agents to change strategy and it is a crucial element of this class of models. The linear approximation permits a simple interpretation of the model dynamics and, for many properties, it is possible to derive analytical results. The generalized non linear dynamics results to be extremely more sensible to the parameter space and much more difficult to analyze and control. The main results for the nature and Self-Organization of the Stylized Facts are, however, very similar in the two cases. The main peculiarity of the non linear dynamics is an enhancement of the fluctuations and a more marked evidence of the Stylized Facts. We will also discuss some modifications of the model to introduce more realistic elements with respect to the real markets.