人工股票市场建模与实验方法及混沌控制研究
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摘要
金融市场本质上是一个开放型的复杂系统,这个观点已经被大多数学者所接受。混沌理论是三大复杂性理论之一,甚至在圣塔菲研究所成立的时候,混沌理论已经等同于复杂性理论。虽然很多学者认识到基于经典金融学理论的方法对于解决金融市场上的各种复杂性问题存在很大的局限性,这些方法大都是以还原论和整体论为指导的,采用从上至下的方式,通过演绎推理建立模型。他们尝试着通过分析这类模型去解释金融市场产生混沌现象的原因,但大都由于这些方法忽视了金融市场要素之间的联系和各个要素的演化过程,因此无法揭示金融市场混沌动力学特征产生背后的本质规律,无论是政府的监管层,还是投资者,都很难从这些研究结论上获得可操作性和有价值的启示。
金融市场与生物系统都是复杂适应性系统,交易者作为市场上的主体,他们为了避免被市场淘汰,需要不断学习,适应市场的变化;而金融市场作为一个复杂的整体,它功能取决于它的各个组成部分之间的相互作用。随着计算机技术的飞速发展,对整个金融市场进行仿真成为可能。这样的人工金融市场可以为本文展现金融市场丰富的混沌动力学特征,这些特征是金融市场各个组成部分相互作用而“涌现”出来的;同时它还可以描述交易者学习进化的过程。人工股票市场中包括能实现其各种功能所必需的参数,这些参数是相互联系的。这样在人工股票市场中,就有可能研究金融市场“涌现”出的混沌动力学特征的形成机理,找出导致混沌现象发生的某些关键因素。这种计算实验金融学将为金融市场的研究人员和风险管理人员提供一个有价值的理论支撑和切实可行的方法。本文就是从系统科学的复杂适应理论出发,从下而上的通过归纳的途径建立中国金融市场的计算机模型,在仿真的基础上,利用实验的方法,对中国金融市场的混沌动力学特征及其内在的本质规律展开研究的,并提出相应的混沌控制措施。
首先,介绍了计算金融学和混沌理论,并分析了传统建模方法和混沌控制方法的缺陷。本文分析了复杂适应理论、基于智能的人工股票市场方法和基于人工股票市场的混沌控制方法。并以传统的金融混沌模型——Duffing-Holms模型为例,指出了数学混沌模型和控制方法在金融市场上运用的局限性。此外,本文还发现了Duffing-Holms模型的一个序参量——外力频率参数,给出了它的周期解的存在性条件。
然后,对中国股票市场的混沌动力学特征进行了全面地考察。本文通过相关维检验、李雅普诺夫指数检验、BDS检验和返回临近(CR)检验对中国股票市场的混沌特征进行了分析,获得中国股票市场是混沌的有力证据。这是本文下面寻找中国股票市场产生混沌动力学特征的内部因素的前提。
接着,构建了具有中国特色的人工股票市场。本文根据中国股票市场在交易者的类型、价格产生机制、股票派息率和市场政策方面的特色,建立了计算机模型,结合遗传算法,对中国股票市场进行仿真,得到了人工金融市场的价格时间序列和收益率时间序列。
在此基础上,检验了人工股票市场上的混沌动力学特征,发现人工股票市场具有和中国股票市场相似的动力学特征。紧接着本文通过对人工股票市场反复实验,对导致股票市场产生混沌现象的关键因素进行分析研究,发现政策因子、噪声交易者、交易者学习进化速度、交易者预测规则集中预测规则的数目和股票市场的流通量是股票市场的序参量,它们的变化会导致市场涌现的动力学特征的改变,并给出了相应的混沌控制建议。
最后,在封闭的和开放人工股票市场中,发现了股票市场所涌现出价格序列不同的演化趋势,以及不同类型交易者拥有的财富的演化路径。在这一部分,本文挖掘出了决定交易者财富多少的关键因素。此外,本文的研究还表明在实行双向拍卖制度的股票市场上,股利不能传递上市公司的信息。这些结论为交易者获得更多的财富和进行合理的投资提供了科学的建议。
Most of researchers have accepted that financial market is essentially a huge open and complicated system. Chaos theory is one of the three complexity theories. Chaos theory even substituted complexity theory when Santa Fe Institution (SFI) was established. Although many researchers knew that there were lots of limits to using methods based on traditional finance theories and directed by reductionism or holism to resolve complexity questions in financial markets. They still build models from up to down and through deductive approaches and they tried to explain why financial markets will be chaotic by analyzing these models. But these models ignore relations between factors and their evolution process in financial markets, so they are incapable to discover essential rules hidden in chaotic dynamical characteristics. Hence neither the government nor investors can obtain any exercisable and valuable revelation from these studies.
Both the financial market and the ecosystem are complex adaptive systems. Investors, as agents in the market, have to learn to adapt themselves to changes of the market and avoid to be washed out. The financial market is a complicated whole and its chaotic dynamical characteristics and its function rely on the interaction effects between different parts of the system. With the rapid development of computer technology, it is possible to emulate a financial market. This artificial financial market can exhibit rich chaotic dynamical characteristics that emerge with the interaction between parts of the financial market. At the same time it demonstrates how investors’knowledge of the financial market evolutes. The artificial financial market includes necessary parameters that are interdependent to implement functions. In this way we can study mechanism of a financial market to come into being chaos and find out key factors that lead to chaos. This computational experimental finance will provide a valuable theory support and a feasible method for finance researchers and risk managers. Setting about complex adaptive theory of system science, this paper builds computer models of Chinese financial market from down to up and through induction approaches. And then we study chaotic dynamical characteristics and intrinsic rules of Chinese financial market by experimenting.
Firstly, we introduce computational finance and chaos theories, and analyze limitations of traditional modeling and controlling methods. This paper analyzes the complex adaptive theory, the intelligent artificial stock market method based and the chaos controlling method based on an artificial stock market. And take the Duffing-Holms model for example, we point out the limitations of mathematic chaotic models and controlling methods applying in financial markets. Besides, we find a order parameter of the Duffing-Holms model——outside force frequency parameter, and present existence conditions of period solution of the model.
Secondly, we analyze roundly the chaotic dynamical characteristics of Chinese stock market. We have tested the chaotic characteristics by using correlation dimension test, Lyapunov exponent test, BDS test and close return (CR) test. The conclusion indicates that Chinese stock market is chaotic. This conclusion is a precondition to find intrinsic factors of chaotic dynamical characteristics of Chinese stock market in the following text.
Thirdly, we create an artificial stock market with Chinese characteristics. Computer models are built in light of characteristics of investors’types, pricing mechanism, dividend and policies of Chinese stock markets. We simulate Chinese stock market with these models and genetic arithmetic. Price time series and return time series of the artificial stock market have been gained.
With foregoing work, we test chaotic dynamical characteristics of the artificial stock market and find that it possesses dynamical characteristics just as real Chinese stock market. Through experimental methods, we study the key factors that lead to chaos of the stock market and discover that policy factors, noise traders, the evolution speed of traders’knowledge, the number of forecasting rules in investors’forecasting rules sets and liquidity are the order parameters of a stock market. Changes of these order parameters will cause the change of chaotic dynamical characteristics of a stock market. We also raise some suggestions to contol chaos.
Finally, this paper demonstrates different evolvement trends of price series emerged from the stock market respectively in a close artificial stock market and an open artificial stock market. This paper also points out the wealth accumulation evolvement paths of different traders’respectively in these two kinds of markets. In this part, we find out key factors that determine the amount of traders’wealth. Besides, we find that dividend can’t transfer information of listed companies in double auction markets. These conclusions provide scientific suggestions for traders to win more wealth and invest reasonably.
金融市场与生物系统都是复杂适应性系统,交易者作为市场上的主体,他们为了避免被市场淘汰,需要不断学习,适应市场的变化;而金融市场作为一个复杂的整体,它功能取决于它的各个组成部分之间的相互作用。随着计算机技术的飞速发展,对整个金融市场进行仿真成为可能。这样的人工金融市场可以为本文展现金融市场丰富的混沌动力学特征,这些特征是金融市场各个组成部分相互作用而“涌现”出来的;同时它还可以描述交易者学习进化的过程。人工股票市场中包括能实现其各种功能所必需的参数,这些参数是相互联系的。这样在人工股票市场中,就有可能研究金融市场“涌现”出的混沌动力学特征的形成机理,找出导致混沌现象发生的某些关键因素。这种计算实验金融学将为金融市场的研究人员和风险管理人员提供一个有价值的理论支撑和切实可行的方法。本文就是从系统科学的复杂适应理论出发,从下而上的通过归纳的途径建立中国金融市场的计算机模型,在仿真的基础上,利用实验的方法,对中国金融市场的混沌动力学特征及其内在的本质规律展开研究的,并提出相应的混沌控制措施。
首先,介绍了计算金融学和混沌理论,并分析了传统建模方法和混沌控制方法的缺陷。本文分析了复杂适应理论、基于智能的人工股票市场方法和基于人工股票市场的混沌控制方法。并以传统的金融混沌模型——Duffing-Holms模型为例,指出了数学混沌模型和控制方法在金融市场上运用的局限性。此外,本文还发现了Duffing-Holms模型的一个序参量——外力频率参数,给出了它的周期解的存在性条件。
然后,对中国股票市场的混沌动力学特征进行了全面地考察。本文通过相关维检验、李雅普诺夫指数检验、BDS检验和返回临近(CR)检验对中国股票市场的混沌特征进行了分析,获得中国股票市场是混沌的有力证据。这是本文下面寻找中国股票市场产生混沌动力学特征的内部因素的前提。
接着,构建了具有中国特色的人工股票市场。本文根据中国股票市场在交易者的类型、价格产生机制、股票派息率和市场政策方面的特色,建立了计算机模型,结合遗传算法,对中国股票市场进行仿真,得到了人工金融市场的价格时间序列和收益率时间序列。
在此基础上,检验了人工股票市场上的混沌动力学特征,发现人工股票市场具有和中国股票市场相似的动力学特征。紧接着本文通过对人工股票市场反复实验,对导致股票市场产生混沌现象的关键因素进行分析研究,发现政策因子、噪声交易者、交易者学习进化速度、交易者预测规则集中预测规则的数目和股票市场的流通量是股票市场的序参量,它们的变化会导致市场涌现的动力学特征的改变,并给出了相应的混沌控制建议。
最后,在封闭的和开放人工股票市场中,发现了股票市场所涌现出价格序列不同的演化趋势,以及不同类型交易者拥有的财富的演化路径。在这一部分,本文挖掘出了决定交易者财富多少的关键因素。此外,本文的研究还表明在实行双向拍卖制度的股票市场上,股利不能传递上市公司的信息。这些结论为交易者获得更多的财富和进行合理的投资提供了科学的建议。
Most of researchers have accepted that financial market is essentially a huge open and complicated system. Chaos theory is one of the three complexity theories. Chaos theory even substituted complexity theory when Santa Fe Institution (SFI) was established. Although many researchers knew that there were lots of limits to using methods based on traditional finance theories and directed by reductionism or holism to resolve complexity questions in financial markets. They still build models from up to down and through deductive approaches and they tried to explain why financial markets will be chaotic by analyzing these models. But these models ignore relations between factors and their evolution process in financial markets, so they are incapable to discover essential rules hidden in chaotic dynamical characteristics. Hence neither the government nor investors can obtain any exercisable and valuable revelation from these studies.
Both the financial market and the ecosystem are complex adaptive systems. Investors, as agents in the market, have to learn to adapt themselves to changes of the market and avoid to be washed out. The financial market is a complicated whole and its chaotic dynamical characteristics and its function rely on the interaction effects between different parts of the system. With the rapid development of computer technology, it is possible to emulate a financial market. This artificial financial market can exhibit rich chaotic dynamical characteristics that emerge with the interaction between parts of the financial market. At the same time it demonstrates how investors’knowledge of the financial market evolutes. The artificial financial market includes necessary parameters that are interdependent to implement functions. In this way we can study mechanism of a financial market to come into being chaos and find out key factors that lead to chaos. This computational experimental finance will provide a valuable theory support and a feasible method for finance researchers and risk managers. Setting about complex adaptive theory of system science, this paper builds computer models of Chinese financial market from down to up and through induction approaches. And then we study chaotic dynamical characteristics and intrinsic rules of Chinese financial market by experimenting.
Firstly, we introduce computational finance and chaos theories, and analyze limitations of traditional modeling and controlling methods. This paper analyzes the complex adaptive theory, the intelligent artificial stock market method based and the chaos controlling method based on an artificial stock market. And take the Duffing-Holms model for example, we point out the limitations of mathematic chaotic models and controlling methods applying in financial markets. Besides, we find a order parameter of the Duffing-Holms model——outside force frequency parameter, and present existence conditions of period solution of the model.
Secondly, we analyze roundly the chaotic dynamical characteristics of Chinese stock market. We have tested the chaotic characteristics by using correlation dimension test, Lyapunov exponent test, BDS test and close return (CR) test. The conclusion indicates that Chinese stock market is chaotic. This conclusion is a precondition to find intrinsic factors of chaotic dynamical characteristics of Chinese stock market in the following text.
Thirdly, we create an artificial stock market with Chinese characteristics. Computer models are built in light of characteristics of investors’types, pricing mechanism, dividend and policies of Chinese stock markets. We simulate Chinese stock market with these models and genetic arithmetic. Price time series and return time series of the artificial stock market have been gained.
With foregoing work, we test chaotic dynamical characteristics of the artificial stock market and find that it possesses dynamical characteristics just as real Chinese stock market. Through experimental methods, we study the key factors that lead to chaos of the stock market and discover that policy factors, noise traders, the evolution speed of traders’knowledge, the number of forecasting rules in investors’forecasting rules sets and liquidity are the order parameters of a stock market. Changes of these order parameters will cause the change of chaotic dynamical characteristics of a stock market. We also raise some suggestions to contol chaos.
Finally, this paper demonstrates different evolvement trends of price series emerged from the stock market respectively in a close artificial stock market and an open artificial stock market. This paper also points out the wealth accumulation evolvement paths of different traders’respectively in these two kinds of markets. In this part, we find out key factors that determine the amount of traders’wealth. Besides, we find that dividend can’t transfer information of listed companies in double auction markets. These conclusions provide scientific suggestions for traders to win more wealth and invest reasonably.
引文
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