Cellular Automata based Artificial Financial Market [chapter]

Jingyuan Ding
2011 Cellular Automata - Simplicity Behind Complexity  
Rational investor hypothesis, efficient markets hypothesis(EMH), and random walk of yield rate are three basic concepts of modern capital market theory. However, it could not be proved that real capital markets are full with rational investors. The theory, which regards the price movement of capital market as random walks, and regards the yield time series as a normal distribution, is not supported by the real statistics data usually. A capital market, in essence, could be regarded as a complex
more » ... system, which consists of masses of investors. Investors make investment decision basing on the public or private information inside or outside the market. The movement of price and volume is the emergency of investors' group behavior. With the sustained growth of computational capabilities and the appearance of complexity science, artificial life, multi-agent system (MAS), and cellular automata (CA) are provided for the modeling of complex system. Researchers got powerful tools to build discrete dynamics model for the capital market for the first time. The Santa Fe artificial stock market(SF-ASM), which is presented by Santa Fe institution in 1970s, is the original version of the artificial financial market(AFM). Modeling for the microstructure of the capital market, made the verification and falsification of economics theories possible. On the part of macroscopic statistical data of the market, a series non-linear dynamic analysis method, such as fractal statistics, had been applied to analysis of financial time series. New research methods, which are used both in microscopic and macroscopic aspects of capital market, help us build brand new dynamic models for capital markets. The appearance of SF-ASM has influenced this area deeply. Most successors are the variety or improvement of SF-ASM. SF-ASM is a kind of MAS, which focuses on simulating heterogeneous investors' investment behaviours. In my opinion, the investment process of an investor can be divided into 2 steps: forecasting and decision. The forecasting step is how an investor considers public or private information inside or outside of the market. And the decision step is how an investor reacts to the prediction. Rational investor hypothesis and various investment decision processes in SF-ASM are just different ways to deal with information. Basing on neoclassicism economics, EMH announce that the price in the market reflects all information, or at least all public information, and that rational investors react to these information in the same way. Multi-Agent based SF-ASM supports heterogeneous investors in reacting to information in various ways, but provides public price as the only information. The fact that information relating to the market is homogeneous and public to each investor can be compared to the gas filling the whole www.intechopen.com Cellular Automata -Simplicity Behind Complexity 360 " c o n t a i n e r o f m a r k e t " . H o w e v e r , a s w e k n o w , i n r e a l c a p i t a l m a r k e t s , e x c e p t p u b l i c information including the announcement, annual report, interest rate etc., there are also inside information, individual attitudes or predictions, and even emotions, which can influence investors' investment. What's more, information is time sensitive. Because nonpublic information may reach investors in different time, the situation of real capital market could be more complex. So SF-ASM is more "efficient" than real capital markets for it's simplifying the description of information. If we describe the non-public information in an AFM model, the interoperation among individual investors can be expressed certainly. As a result, the cellular automaton (CA) is adopted. Classical CA is a kind of large scale discrete dynamical systems. Each cell in CA can interoperate with neighbors in a local scope, which is defined by CA's neighborhood. Yiming Wei, Shang-jun Ying, Ying Fan, and Bing-Hong Wang presented a CA based AFM in 2003. In this model, the local interoperation of CA is used to describe the spread of the herd behavior in capital markets. However, the neighborhood of this CA based AFM is still classical Moore neighborhood. All the investors in this AFM have the same simple investment behavior rule. The pricing mechanism of the market is far from the realistic markets. In real capital markets, as we know, the non-public information spreads through the investors' social network, rather than 2-D lattice. The connectivity, diameter, and degree distribution of the social network can decide the speed and scope of the information spreading. Furthermore, social network is not a fix, but dynamic structure. According to the above reasons, combining the feature of multi-agent system and complex network, we extend the definition of CA in following aspects in this chapter: Neighborhood with network topology is adopted in CA; Structure of neighborhood is no more fixed, and will change following the neighborhood evolution rule; Cells in CA are no more homogeneous, and each cell has its own state transfer function with the same interoperation interface. Combining the above extensions of CA, as well as the other researchers' research on cellular automata on networks (or graph automata), we present a formal definition of CA on networks. On the basis of CA on networks, a new artificial financial market modeling framework, Emergency-AFM (E-AFM), is introduced in this chapter. E-AFM provides all standard interfaces and full functional components of AFM modeling. It includes classification and expression of information, uniform interfaces for investors' prediction and decision process, uniform interface for pricing mechanism, and analysis tools for time series. E-AFM is a modeling framework for any kind of AFM. By instantiating the investors' asset structure, neighborhood network, behavior rules of investors, and pricing mechanism, we can get a specific AFM model. After an AFM model is simulated, we can get a price and volume time series in standard format just like real capital markets. Analysis tools provided by E-AFM, such as Hurst exponent and Lyapunov exponent, can be used to measure the fluctuation feature of price/yield time series. We can compare the simulation data with the real capital market data. Also we can find the relationship between the fluctuation feature and the topology of social networks. In the rest of this chapter, an E-AFM based AFM model is introduced. This model is a simple model which is designed to find the relationship between the fluctuation feature of price time series and the degree distribution of the social network (neighborhood of CA). The statistics feature of neighbourhood structure is observed and compared with the fluctuation feature of price/yield time series. It is not a perfect model to get a new capital theory, but we can still realize how cellular automata can help us to do research in financial area. www.intechopen.com Cellular Automata based Artificial Financial Market 361
doi:10.5772/15805 fatcat:63hx5qrmq5cwvcj5s77zmu7mp4