基于元胞自动机的金融市场建模研究

发布时间：2018-04-30 23:35

本文选题：元胞自动机 + 金融市场　；参考：《北京交通大学》2012年博士论文

【摘要】：近年来,研究者对来自金融市场的历史数据进行统计分析,发现得到的结论与经典的金融市场理论、模型之间存在着偏差,这些偏差对金融市场理论的三大假设：理性人假设、有效市场假设和随机漫步假设提出了挑战,人们迫切需要新的视角和工具来对金融市场这一复杂系统进行重新的研究。20世纪80年代以来,复杂性科学兴起,以复杂适应理论为代表的一大批研究复杂系统的方法论为金融理论的进一步发展提供了契机。本文使用元胞自动机这一研究复杂系统的有力工具来对金融市场进行建模,希望可以解释经典金融理论、模型、方法不能够解释的市场特征。文章的主要内容共分为四个部分：首先,利用标准普尔500和上证A股的历史数据,分析了国际与国内金融市场中与经典金融市场理论不相符合的统计特征,这些统计特征包括收益率分布的厚尾特性、收益率分布偏度的负性、日收益率之间的不相关性、收益率和交易量之间的关系、收益率波动的随机性、波动聚集性和长时记忆性。同时比较分析了国际和国内市场在这些统计特征上的异同。其次,利用元胞自动机模型建立了一个期权定价方法。论文介绍了Black-Scholes模型、二叉树模型、以及有限差分方法这些经典的期权定价模型,并探讨了二叉树模型和有限差分方法与元胞自动机之间的联系。明确了期权定价问题的核心就是对基础资产价格的波动率建模。基于元胞自动机的期权定价模型就是通过对市场参与者之间交互行为的模拟,来模拟金融市场中基础资产价值的波动率变化的随机性。论文使用Black-Scholes模型验证了这种定价方法不仅仅具有可行性,而且更进一步的发现模型模拟出了厚尾性这一重要的统计特征,说明基于元胞自动机的期权定价模型相对于Black-Scholes模型更加有效。第三,提出了一个基于元胞自动机的异质金融市场模型,该模型将金融市场中的交易者分为基础资产价值导向和技术分析导向两类。模型利用一定的学习规则使得交易者可以在这两种类型之间相互转化。模型通过交易者之间的相互交互行为来模拟金融市场的整体行为。论文分析了基于元胞自动机的异质金融市场模型的随机性的来源、均值回归特性、金融泡沫的产生和破裂、模型的平稳性、模型与Ornstein-Uhlenbeck之间的关系、模型与GARCH模型族之间的关系。通过对基于元胞自动机的异质金融市场模型模拟的数据进行统计分析,发现模型可以很好的模拟出收益率分布的厚尾特性、收益率分布偏度的负性、收益率和交易量之间的关系、收益率波动的随机性、波动聚集性这些和经典金融市场模型不相符合的统计特征。同时论文还讨论了如何向模型中加入更多的异质特性。最后,研究了异步元胞自动机的可能性,并从同步性、多重性和随机性三个方面将异步元胞自动机分为八类；论文分析了金融市场中的异步性,认为金融市场的异步性主要包括信息扩散的异步性、市场参与者竞价的异步性和完成市场交易的异步性,并从这三个方面出发,初步设计了基于异步元胞自动机的金融市场模型。论文以元胞自动机为工具设计并实现了期权定价模型和异质金融市场模型。期权定价模型计算得到的期权价格和使用公式计算的结果十分接近。异质金融市场模型模拟得到的市场价格变化可以解释许多经典金融理论不能解释的现象,例如收益率的厚尾特性、金融泡沫的产生和破裂等等。本文还初步设计了基于异步元胞自动机的金融市场模型。这些模型和结论说明元胞自动机可以很好地反映金融市场中的随机性,模拟出金融市场参与者的市场行为。因此可以说元胞自动机是探索金融市场复杂性的强有力的工具。同时,这种自下而上的,基于规则的建模方法也为探索其他复杂系统提供了新的思路和方法。
[Abstract]:In recent years, the researchers have analyzed the historical data from the financial market, and found that there is a deviation between the conclusions and the classical financial market theory. These deviations have challenged the three hypotheses of the financial market theory, the rational man hypothesis, the effective market hypothesis and the random walk hypothesis. The complex system of financial markets has been re studied by the perspective and tools. Since the 80s.20 century, complexity science has emerged. A large number of methodology of complex adaptive theory, represented by complex adaptation theory, provides an opportunity for further development of financial theory. This paper makes the study of complex systems with cellular automata, a complex system. The main contents of the article are divided into four parts: the modeling of the financial market by force tools, and hope to explain the market characteristics that the classical financial theory, the model, the method can not explain.
First, using the historical data of the standard & Poor's 500 and the A shares of the Shanghai stock market, we analyze the statistical characteristics that are not consistent with the classical financial market theory in the international and domestic financial markets. These statistical features include the thick tail characteristics of the yield distribution, the negativity of the yield bias, the unrelevance between the daily income rate, the rate of return and the volume of transactions. The relationship between the volatility of return rate, volatility aggregation and long term memory is also analyzed. The similarities and differences between the international and domestic markets are compared and analyzed.
Secondly, a option pricing method is established by the cellular automata model. The paper introduces the Black-Scholes model, the two forked tree model, and the finite difference method, and discusses the relationship between the two tree model and the finite difference method and the cellular automata. The core of the option pricing problem is clarified. The option pricing model based on cellular automata is to simulate the randomness of the volatility of the underlying asset value in the financial market by simulating the interaction between the market participants. The paper uses the Black-Scholes model to verify that the pricing method is not only feasible, but also proved that the pricing method is not only feasible. Furthermore, the further discovery model simulates the important statistical characteristics of thick tailing, indicating that the option pricing model based on cellular automata is more effective than the Black-Scholes model.
Third, a heterogeneous financial market model based on cellular automata is proposed. The model divides the traders in the financial market into two categories of basic asset value orientation and technical analysis guidance. The model makes use of certain learning rules to enable traders to transform each other between the two types. Interacted to simulate the overall behavior of the financial market. The paper analyzes the origin of the randomness of the heterogeneous financial market model based on the cellular automata, the mean regression characteristics, the generation and rupture of the financial bubble, the stability of the model, the relationship between the model and the Ornstein-Uhlenbeck, the relationship between the model and the GARCH model family. The data of the heterogeneous financial market model of cellular automata are statistically analyzed. It is found that the model can well simulate the thick tail characteristics of the yield distribution, the negativity of the yield distribution bias, the relationship between the rate of return and the transaction, the randomness of the volatility of the return, the volatility aggregation, and the classical financial market model. At the same time, the paper also discusses how to add more heterogeneity to the model.
Finally, the possibility of asynchronous cellular automata is studied, and asynchronous cellular automata is divided into eight categories from three aspects of synchronization, multiplicity and randomness. The asynchronism in the financial market is analyzed. The asynchronism of the financial market mainly includes the asynchronism of information diffusion, the asynchrony of the competition of market participants and the completion of the market intersection. From the above three aspects, we design a financial market model based on asynchronous cellular automata.
The option pricing model and the heterogeneous financial market model are designed and realized by the cellular automata. The option pricing model calculated by the option pricing model is very close to the results calculated using the formula. The market price change from the model of the heterogeneous financial market model can explain the phenomenon that many classical financial theories can't explain. This paper also preliminarily designs a financial market model based on asynchronous cellular automata. These models and conclusions show that cellular automata can well reflect the randomness in the financial market and simulate the market behavior of the participants in the financial market. Cellular automata is a powerful tool for exploring the complexity of financial markets. At the same time, this bottom-up, rule-based modeling method also provides new ideas and methods for the exploration of other complex systems.

【学位授予单位】：北京交通大学
【学位级别】：博士
【学位授予年份】：2012
【分类号】：F224;F830.9

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