Complexity, Agents, and Finance

Blake LeBaron

International Business School, Brandeis University

February 2009

These short notes are an exploration into how ideas from complexity and agent-based modeling impact how I think about financial markets. They come from my experience (almost 20 years now) of using nonlinear dynamics and agent-based modeling as applied to financial market problems. I do believe this gives one a view of the world which is different from traditional approaches. Now with global markets in a state of uncertainty, there are many good reasons for looking to complexity ideas to see what they tell us.

Complex adaptive systems represent an interdisciplinary approach to many different dynamical systems across a wide range of fields both in the physical and social sciences. While there is no accepted definition, they have at their core large interconnected systems with many interacting components. Macro level analysis of large scale systems was traditionally a straight forward implementation of laws of large numbers. Dynamics in these systems can be inferred from the dynamics of ensembles or system averages. Often this amounts to summarizing the system's state using distribution means or variances. Interactions of the components in complex systems are often nonlinear which makes traditional methods of analysis ineffective. Dynamics often reveal emergent phenomena, or rich patterns that are not obviously connected to micro level components of the system. These dynamics are usually nonlinear in nature, in that they display features which are much more complex than simple trends or cycles. Also, they can display very different patterns depending on the exact state of the system.

Financial markets clearly meet the criteria for being a complex adaptive system. However, their study has been more difficult than others. This is mainly due to difficulties in constructing heterogeneous agent models which are both rich enough to reveal interesting dynamics, but simple enough to be tractable in terms of gaining intuition about what is happening. Researchers have generally plowed ahead here using various forms of agent-based technologies which use models attempting to build bottom up behavior from individuals usually modeled from computational tools. These models give us a different perspective on what a financial market looks like. Under the hood they are not characterized by anything that looks remotely like a static equilibrium model from economics or finance. Agents are continually adjusting and adapting their strategies to continual change. At the macro level the markets faithfully replicate most empirical features common in large financial markets. It is premature to claim that agent-based simulations provide a definitive model of financial markets either near equilibrium, or under stress. However, observation of these systems should be used as computational thought experiments for both researchers and policy markers. The computer pushes the envelope in many situations, telling us what might happen, or what dangers may lurk in places not explored by more standard approaches.

This sequence of expanding notes will explore some ideas in finance from the perspectives of complex systems, and agent-based modeling. They will attempt to make contact with the key policy questions that are being struggled with today on how to reform financial markets. This should not be viewed as a tutorial on agent-based financial markets, since I have already done this before. This is more a set of somewhat connected thoughts on the perspective these ideas have on ways we can interpret the world.