The efficient market hypothesis (EMH) had emerged in the mid-1960s to gain general acceptance as a prominent financial theory. The main idea of the EMH is that asset prices are always at the correct value of the asset, markets move toward equilibrium, and after reaching equilibrium they remain in this state until influenced by an unexpected exogenous shock. Thus, according to this theory, financial markets cannot generate their own internal forces to disrupt an equilibrium, and large price changes are just the result of markets responding to new information from the outside or to changing fundamentals. Therefore, according to EMH, there is no room for asset price bubbles or crashes to occur.Footnote 1
However, history and past data show that the EMH is not always successful in explaining phenomena in financial markets. From the Dutch tulip bubble in 1626, the British South Sea Company bubble, the French Mississippi Company bubble of the early 18th century, and the Japanese bubble in 1980s to recent U.S. sub-prime mortgage and the financial crisis of 2008, bubbles and crashes in financial markets have occurred and continued to occur.
In a broader context, the failure of the mainstream economic theory to predict financial crises has been pointed out (Colander et al. 2009; Buchanan 2009), such that while it has been partially successful in predicting events in the near future using past data, it has failed in the face of the changes of a much bigger scale. The theory of dynamic stochastic general equilibrium (DSGE) also has limitations due to its dependence on strong assumptions, such as perfect rationality of the representative agent and the predetermined equilibrium concept for analytic solutions. In addition, because they exclude crises of the type that have occurred before and that we are experiencing now, it is not possible to predict a crisis using these models. Now, there is a growing recognition that an alternative theory or model is needed to explain the types of events that conventional economic models have never sufficiently explained. Agent-based modeling (ABM) has been proposed as an alternative (Farmer and Foley 2009; LeBaron 2006; The Economist 2010).
ABM is a computational methodology that allows an analyst to create, analyze, and experiment with artificial worlds composed of agents that interact within a specific environment.Footnote 2 It is characterized by key assumptions such as bounded rationality of agents, routine-based or adaptive behavioral rules, heterogeneity of agents, and learning process (Yoon and Lee 2009). Namely, in contrast to the DSGE, ABM allows a high degree of heterogeneity of agents and takes a bottom-up approach which assigns particular behavioral rules to each agent and generate dynamic path of an economy out of interaction among agents. In this light, ABM is appropriate for analyzing the financial market as an outcome of heterogeneous agents and their interactions and for investigating economic phenomena such as financial crisis, which is hard to explain using mainstream economics tools.
Some previous studies have analyzed the financial markets based on ABM. The Santa Fe Artificial Stock Market, SF-ASM, is one of the earliest representative models. The SF-ASM model has evolved from the initial version of Palmer et al. (1994) and LeBaron et al. (1999) to the modified version by Ehrentreich (2004). Palmer et al. (1994) set up a simple stock market model where independent adaptive agents trade stock on a central market. They showed that price can display bubbles, crashes, and continued high trading volume. LeBaron et al. (1999) present an experimental computer simulated stock market to show that for some parameters the market generates interesting features, which appear to replicate some of those found in real financial time series data.
A growing number of models have been developed to consider the heterogeneity of the agents and interactions among them, such as Chiarella and Iori (2002), Chiarella et al. (2006), Chiarella et al. (2009), and Malek and Ezzeddine (2011). Chiarella and Iori (2002) show how the trading strategies of noise traders, fundamentalists and chartists have an effect on the price, bid-ask spreads, trading volume and volatility; Fundamentalists are agents who make trading decisions with a belief that an asset has its own intrinsic value (equilibrium price) at any point of time, whereas chartists use past price trends as basis for decisions with a belief that the history of the price changes is useful information for making meaningful predictions for the future price of the asset. They show that the presence of chartist plays a critical role in the volatility of price and trading volume, and investigate the correlation between them. Chiarella et al. (2009) set up the model with agents assumed to have three components of the expectation of future asset returns, namely fundamentalist, chartist and noise trader, and analyzed the impact of these three components of trading strategies on the statistical properties of prices and order flows. Through this model, it turns out that fat tails are caused by the chartist strategy. Malek and Ezzeddine (2011) consider three different types of investors; fundamental agents, irrational agents, and loss adverse agents, and show that irrational investors can explain the excess volatility of stock prices. They focus on the volatility puzzle which is hard to explain with traditional financial theories including efficient market hypothesis. Chiarella et al. (2006) consider a financial market with both a risky asset and a safe asset with a view to explain asset price and wealth dynamics as a result of the interaction between two groups of agents, fundamentalists and chartists.
Besides the papers which consider heterogeneity of the agents, the studies on asset market using ABM have been extended in a variety of ways. Harras and Sornette (2011) focus on the source of information. They endogenize three sources of information to the decisions of agents to show that a random sequence of the same news pushes price in one direction, and that through the coordination process among agents, the price reaches to an unsustainable level. Also, they show that once the agents have invested all their cash into the stock, just a little negative news can cause the price to collapse.
Taken together, the previous studies on asset market based on ABM mainly focused on the heterogeneity of agents and their interactions, and some of these studies were extended to consider the source of information that agents can access. Now, while the aim of the current study is also to explain the mechanisms of how bubbles and crashes emerge in asset markets with heterogeneous agents based on the ABM, our distinctions are as follows. First, while most of the previous literatures considered the heterogeneity of agents in forming expectations for future asset price or returns, and explained the dynamics of asset price as a consequence of the presence of chartists (Chiarella and Iori 2002; Chiarella et al. 2009), we expand upon this by considering the role of different expectations for the ‘tipping point’ by each agent as a cause of the collapse of the asset prices in the financial markets. As previous studies have pointed out, chartists can be expected to buy additional assets even at the high price level if they believe that the asset price will rise further. These behaviors of agents push the market price to a higher level, and bubbles can occur. However, during the process, if the price rises above certain level that the agent believes to be the maximum, the agent will change his behavior from buying to selling due to a concern for loss of capital. Namely, each agent has different or heterogeneous expectations about the ‘tipping point’ for the asset price. These expectations can affect the dynamics of asset price. However, so far, most of the previous studies have not considered this. In this paper, we reflect this aspect into the model to investigate how different expectations about tipping point could have an effect on the dynamics of an asset price. Furthermore, we also allow the herding behavior such that some agents share the same expectations about the price levels.
Second, we do not divide agents into either fundamentalists or chartists. In the real world, if agents have access to information about both the fundamental values of the asset and the historical price change data, they will use both of these to predict the future price rather than using just one type of information. Thus, we assume that each agent has the weight for each component used for anticipating the future prices. Third, we use simple but intuitive trading rules for each agent, rather than assuming certain types of expected utility functions such as CARA (Arthur et al. 1997; Chen and Yeh 2001; Lettau 1997) and CRRA (Bullard and Duffy 2001; LeBaron 2001; LeBaron 2006; Chiarella et al. 2006), to avoid adding unnecessary assumptions to derive simple demand function from it.
The ABM simulation in this paper is to show how the heterogeneous expectations across groups of agents about the tipping point affect price dynamics and maximum price level. It will be first shown in a benchmark model without grouping of agents where every single agent have different expectation that the collapse of the price does not emerge automatically, and price fluctuations are often small and even some (seemingly) flat intervals appear. However, this pattern of dynamics for asset price change when we reduce the heterogeneity in forming the expectations about tipping points and allow herding behavior among agents. In other words, we investigate how herding behaviors of agents can affect asset price dynamics by divide agents into several groups which share the same expectation about the tipping points, so that agents in the same group move together or collectively but agents in different groups behave differently. By changing the size of groups (number of agents in each group) or changing the number of groups, we will generate a case of extreme instability where the asset price fluctuates rapidly in large amount within a short period of time. Basically, price dynamics show higher volatility when more agents share same thresholds, which is the case of a smaller number of groups or larger size of members in each group. In sum, we show that bubble and burst of prices is more like to emerge when heterogeneous expectation about prices are combined with herding behavior among agents, so that agents in the same group share the similar expectations about the price changes.
This paper is organized as follows. In section The model, we present a basic model, and introduce the formations of the expectation for the asset price, trading rules, and equations for price determination. Section Simulation analysis provides the simulation results. Finally, section Concluding remarks provides a conclusion.