Quantitative Finance for Physicists

Chapter 12

Agent-Based Modeling

of Financial Markets

12.1 INTRODUCTION

Agent-based modeling has become a popular methodology in

social sciences, particularly in economics.

1

Here we focus on the

agent-based modeling of financial markets [1]. The very idea of

describing markets with models of interacting agents (traders, invest-

ors) does not fit well with the classical financial theory that is based

on the notions of efficient markets and rational investors. However, it

has become obvious that investors are neither perfectly rational nor

have homogeneous expectations of the market trends (see also Section

2.3). Agent-based modeling proves to be a flexible framework for a

realistic description of the investor adaptation and decision-making

process.

The paradigm of agent-based modeling applied to financial markets

implies that trader actions determine price. This concept is similar to

that of statistical physics within which the thermodynamic (macro-

scopic) properties of the medium are described via molecular inter-

actions. A noted expansion of the microscopic modeling methodology

into social systems is the minority game (see [2] and references therein).

Its development was inspired by the famous El Farol’s bar problem [3].

This problem considers a number of patrons N willing to attend a bar

with a number of seats N

s

. It is assumed that N

s

< N and every patron

prefers to stay at home if he expects that the number of people

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