Financial Agent-Based Modeling
Financial theory and economics in general as they have evolved over the past century have adopted the modeling framework of physics and standard mathematics, which is known to be a reductionist framework. Much of current financial theory is based on linear assumptions and top-down equation-based models. Dynamic stochastic general equilibrium models are a paragon of this approach – an equation based macro rule with a limited number of variables that are designed to describe how the whole system works based upon rational expectations of the agents in the system. This approach involves a degree of model expectation; meaning the agents are expected to act as if they understand the model so that the agents fit into the overall model. The general approach is that of aggregating over representative agents to achieve a general equilibrium that can be captured in a single global rule.
Just as Newtonian physics still works as an approximation for most physical motion, for much of science, economic and finance the equilibrium top-down approach works as a rough approximation. However just as we know that Newtonian physics is a shortcut description of a more complex underlying physical reality of general relativity, so too these general equilibrium models are a shortcut for a more complex underlying economic and financial reality. Just as we have to switch from Newtonian physics to general relativity or quantum physics to talk about certain phenomena in our universe, we also have to shift the paradigm within finance if we are to approach important economic phenomena, moving from top-down general rules and equilibrium to bottom-up local rules and nonequilibrium processes of change.
What these general equation based models do not allow for is the reality of how people act and interact locally to create emergent bottom-up patterns based upon local rules; which is to a certain extent how markets work. People find themselves with some set of rules, some kind of local information, and then make their decisions, the interaction of these decisions lead to the overall outcomes in the market. Previously this vision of the world was not possible for our scientific and mathematical models to deal with because it involves massive amounts of free parameters and information. Prior to the advent of computer simulations, we could only write global rules and hope that the empirical data fitted into it, but today new models from complexity theory dealing with self-organization and emergence coupled with computer simulation are changing this.
Dealing with heterogeneous agents making local decisions creates many parameters; it is a high-dimensional problem and this is why large amounts of data and computer models are needed. With computers, we can define bottom-up models, where we start by asking what rules the agents are acting under and then simulate that leading to interaction and emergence. Solutions are no longer well defined and closed, they are more like patterns. We are trying to simulate the rules, actions, and interactions of agents looking at how overall patterns are created and change over time.
One of the key premises of complex systems theory is that global coordination and complex behavior can emerge out of very simple rules governing the interaction between agents on the local level without the need for centralized coordination. At the heart of this is the question of how agents synchronize their state or cooperate to create local patterns of organization. We see many examples of self-organization within complex adaptive systems that are composed of elements following simple rules. For example, swarms of fireflies who may start out flashing their light in a random fashion with respect to each other come, through their interaction, to coordinate their behavior into an emergent pattern of the whole swarm flashing in synchrony.
This type of self-organization can be modeled using agent-based models (ABM) where agents with simple rules are programmed into a computer, the program is left to run and out of the interaction between these simple agents we see emerging surprisingly dynamic patterns that are able to stay evolving over prolonged periods of time to produce novel behavior. This agent-based modeling approach helps to capture important aspects to financial markets that are left out of equation-based models; most importantly this includes interconnectivity. As systems become more complex we get more horizontal peer interactions which allow for the formation of patterns based upon local interaction only. The fact that actors are interacting with others locally and those specific interactions and the context they create becomes important to the overall workings of the system. Likewise, this approach can allow for a diversity of motives and rules under which the members make decisions and act.
By incorporating local interactions and feedback we can begin to see emergent patterns such as attractors. An attractor is a particular set of states towards which any new component within the system will be drawn as it becomes a default. Cities are good examples of this. By having such a high density of people, they reduce transaction costs, increase economic coordination and leverage economies of scale as they become an attractor for anyone in the locality of the city looking for work, trade or business opportunities. We might cite Hong Kong as an example. Having offered itself as a center for free trade during the colonial era, it managed to reach a critical mass to become an attractor for trade and finance within East Asia. But without global regulation and coordination, we will typically get a number of different local attractors forming. For example, Hong Kong is just one attractor within the global financial system. We also have New York, London, Tokyo, Shanghai, etc. Each of these is a different attractor that has emerged from their local context and now has to compete within this global environment. These attractors make the system’s topology heterogeneous.
By allowing for the importance of local interactions agent-based models allow for self-organization and this gives rise to new levels of organization; what are called integrative levels. It is out of this self-organization that we get the emergence of institutions from the micro-level of a small local market to large business organizations, industries, economies and ultimately our whole global market economy, which is a complex adaptive self-organizing system that has evolved over thousands of years.
By looking at the economy and financial markets as a self-organizing system, we can begin to recognize these emergent patterns that are not identifiable when we use standard linear models where we simply aggregate up from the micro-level. With self-organization, we can get non-equilibrium and the emergence of attractors on different levels, with these attractors having their own emergent internal dynamics, meaning they can’t just be abstracted away or derived from simple aggregations of lower level phenomena, and they are very important to the behavior of the system.
Whereas equation based models are always looking for equilibrium points with which to model the market, agent-based models do not do this, thus they allow for non-equilibrium outcomes and continuously novel dynamic behavior in the system. Agent-based models do not require that the system comes back to some form of overall equilibrium and relaxing this constraint can enable a much more realistic vision of markets.
As Brian Arthur states in his paper Out-of-Equilibrium Economics and Agent-Based Modeling1 “Standard neoclassical economics asks what agents’ actions, strategies, or expectations are in equilibrium with (consistent with) the outcome or pattern these behaviors aggregatively create. Agent-based computational economics enables us to ask a wider question: how agents’ actions, strategies, or expectations might react to—might endogenously change with—the patterns they create. In other words, it enables us to examine how the economy behaves out of equilibrium when it is not at a steady state. This out-of-equilibrium approach is not a minor adjunct to standard economic theory; it is economics done in a more general way.”
In 1988 Brian Arthur and John Holland at the Santa Fe Institute built an agent-based model of the US stock market.2 They built a computer model with agents as investors who were trying to form a hypothesis about how the market works; allowing them to start with a random hypothesis and adapt and learn over time if they did not make money they would replace their model with ones that improve over time. These agents were not rational or uniform and they could learn. After running the computer simulated model they found the market looked similar to the standard equilibrium model, but over time they came to see out of equilibrium solutions. When they ran the simulation long enough they started to see little bubbles and crashes and periods of random high volatility that were followed by periods of volatility that was low. They saw all the same Autocorrelations and cross-correlations that one would see in real markets.
After almost two centuries of studying equilibria economists are beginning to study the emergence of equilibria and the general evolution of patterns in the economy. That is, we are starting to study the economy out of equilibrium through a computer-based algorithmic approach. ABMs give us an inherently dynamic vision of markets, as patterns are continually being created and recreated through endless computations across complex networks of interaction, just as we see in the real world. When seen in this way the economy shows itself not as a mechanical, deterministic system always moving towards stability and equilibrium but instead as continuously evolving and creating new structures and patterns.
Tuvalu.santafe.edu. (2018). [online] Available at: http://tuvalu.santafe.edu/~wbarthur/Papers/OutofEquilPaper-SFI.pdf [Accessed 9 Aug. 2018].
Www2.econ.iastate.edu. (2018). [online] Available at: http://www2.econ.iastate.edu/tesfatsi/blake.sfisum.pdf [Accessed 9 Aug. 2018].