Reseach On The Financial Market Modeling Based On The Cellular Automata

In recent years, researchers analyzed the historical data from the financial markets. They found that the statistical result is different from the classical financial theories, models, and methods. The difference is challenging the three hypotheses which are rational people hypothesis, efficient market hypothesis and random walk hypothesis. We need new perspective and tools to re-study the financial market as a complex system. The rise of complexity science and the methodology to the complex system is an opportunity to the development of the financial theories. In this dissertation, the cellular automata are used as a tool to modeling the financial markets. We hope this tool will explain the markets characteristics which the classical theory is failed to explain. The main contents of the article are divided into four parts:Firstly, the historical data of S&P500and Shanghai A share is used to analyze the statistical characteristics domestic and aboard which does not meet the classical financial market models. These characteristics include the fat tail of return's distribution, negative skewness, irrelevance between daily returns, relationship between return and trading volume, the randomness of volatility, volatility cluster, and long memory. Meanwhile, the dissertation also analyzes the difference between domestic markets and aboard markets.Secondly, an option pricing method is proposed by using the cellular automata in this dissertation. The author explores the connections between the cellular automata and the binomial tree model, and finite difference method, and discusses that the key problem of the option pricing is the modeling of the volatility of the underlying asset. The option pricing method based on the cellular automata emulates the interact behaviors between the market participants, and emulates randomes of the volatility of the underlying asset. The author uses the Black-Scholes model to test the feasibility of the option pricing method. At the same time, the method can reflect the one of the most important statistical characteristic:fat-tail, so the option pricing method based on the cellular automata is also effective, compared with the Black-Scholes model.Thirdly, a cellular automata based heterogeneous financial market model is proposed in this dissertation. In this model, the market participant id divided in to two categories which are the fundamentalists and chartists. A learn rules is used to make sure all the market participant can convert in these two categories. The method emulates the interact behaviors between the market participants, and emulates the overall market behavior. The author analyzes the randomness sources, mean-reverting property, bubble happen and bust, and stationary of this model. The author analyzes the relationships between cellular automata based heterogeneous financial market model and the Ornstein-Uhlenbeck model and GARCH models. The data simulated by the financial market model is fit the characteristics such as the fat tail of return's distribution, negative skewness, relationship between return and trading volume, the randomness of volatility, and volatility cluster, which the classical theory is failed to explain. How to add more heterogeneity into the model is discussed in this dissertation.Finally, the possibility of asynchronous cellular automata is discussed in this dissertation. The author divides the asynchronous cellular automata into eight categories by the synchronicity, Multiplicity and randomness. The asynchrony of the financial market is analyzed, and the author believes the asynchrony of the financial market is consist of the asynchrony of the information diffusion, the asynchrony of buying/selling actions and the asynchrony of transaction completion. According the three asynchronies, an asynchronous cellular automata based financial market model is preliminarily designed.In this dissertation, by using the cellular automata as a tool, an option pricing model and a heterogeneous financial market model are proposed. The result of the option pricing model is close to the result calculated by the formula. The simulation of heterogeneous financial market model can explain many phenomenons which can not be explained by the classical theory, such as the fat-tail of return and the bubble happen and bust. The author also preliminary designs the financial market model based on the asynchronous cellular automata. These models and conclusions indicate that cellular automata have a ability to show the randomness of the financial markets and simulate the behaves of the participants in the financial maket. So we can conclude that the cellular automata are a powerful tool to explore the complexity of the financial market. Meanwhile, this moelding method which is bottom-up and based on the rules provides a new perspective for the exploring the complex system.