【作者】 刘伟；

【导师】 郑伟安；

【作者基本信息】 华东师范大学 ， 概率论与数理统计， 2007， 博士

【摘要】 自从资本市场出现以来,对证券价格的分析方法也随之诞生。经过一百多年的应用与发展,技术分析与基本面分析一起形成了金融市场中两大重要的投资分析流派。其中,技术分析是根据证券市场中信息的历史数据,来预测证券价格未来的变动,以指导人们进行交易,它所运用的分析工具是技术指标。作为一种投资手段,技术分析在实际投资指导中得到了非常广泛的应用。然而由于长期以来,技术分析缺乏完善的理论基础,给人造成一种主观判断的印象,所以它始终是人们争论的焦点,争论的核心就是技术分析是否真正有效。在股票市场里,实际的技术分析人员将每天的股价作为一个样本,然后根据某一个现象发生的样本数的频率来推断股票的走势的概率,由此产生了很多技术分析指标,例如布林带,RSI,ROC,……。然而这其间存在着一个不容忽视的问题,即这些股价均不独立,所以到目前为止,尚未有统计理论可以用来支持技术分析。在金融数学里,股价只被看成是一个随机过程的一根样本轨道,这样一只股票的一组股价的实现只是一个零概率事件,分析起来当然也就毫无意义。本文证明了股票市场中,技术分析指标可以从现有的股价模型(例如Black-Scholes模型、随机波动率模型)出发,用平稳过程的理论加以解释。我们发现,那些最重要的技术指标都是平稳过程或其函数变换,而平稳过程可以统计其频率是已有的结论。本文从这个观点出发,为股票价格的技术分析提供了理论依据。全文一共分为七个部分进行阐述。第一部分,回顾股票市场中已有的分析方法,介绍技术分析与基本面分析的定义及其发展历程,以及实际股票市场中的技术人员与从事相关金融理论工作者的研究方法,同时提出了本文主要的研究思路。第二部分,引进金融数学中用来描述股票价格行为的两种常用的连续模型,Black-Scholes模型和随机波动率模型,介绍这两种模型的产生发展背景,给出在本文中的具体公式表达。第三部分,介绍几种被广泛使用的技术分析指标(布林带、RSI、ROC)的定义,以及它们在实际投资中用来指导股票交易的应用法则,并以美国股票市场上几支重要的股票(DIA、QQQQ、SPY)为例,给出它们的技术指标数据统计结果。第四部分,从Black-Scholes模型出发,给出由技术指标确定的随机过程的性质,以及相关的大数定律。第五部分,从随机波动率模型出发,给出一种渐近平稳过程的定义,以及相关的大数定律。同时讨论了由技术指标确定的随机过程的渐近平稳性质和相应的大数定律。第六部分,从Black-Scholes模型出发,给出一系列随机过程的平稳分布的分布直方图的模拟结果,并给出由实际股票价格得到的分布直方图。第七部分,对股票模型进行假设检验。从技术分析指标出发,否定了股票服从指数levy过程的假定,并给出了进一步的研究方向。更多还原

【Abstract】 Many methods to analyze stock price have been developed since the capital market appeared. Through the application and development for more than 100 years, the technical analysis and basic situation analysis have become two important investment directions in the financial market. The technical analysis is based on the historical data of the information in stock market, which can predict the fluctuation of stock price in the future and guide people how to bargain. The tool in technical analysis is technical indicators. As a kind of investment means, the technical analysis gets an extensive applications in actual instruction. However, because of being lack of perfect theoretic foundation for a long time, the technical analysis is always regarded as a kind of subjective judgment. So the discussion about it is always hot, the issue of which is the effectiveness of the technical analysis is true or not.This paper proves that the technical analysis of the stock market can be explained by the stationary process theory, namely, the validity of some indicators can get interpretation from the existing stock price model (for example Black-Scholes model and stochastic volatility model). In the stock market, actual technical analysts look the stock prices everyday as one sample and according to the frequency of occurrence of a certain phenomenon they predict the developing trend of stock price. A lot of technical indicators are created by this way. For example, BOLL, RSI, ROC. However there is a problem which can not be ignored, namely all these stock prices are not independent. So up to now there isn’t any statistical theory can be used to support technical analysis. In financial mathematics, a series of stock prices is regarded as a sample path of stochastic process. Thus the realization of these stock prices is only an event with zero probability. But we discover that, those most important technical indicators are all stationary processes or their functional transformations. However, stationary process can be computed the frequency is well known. From this point, we provide the theoretic basis for technical analysis of stock price. The paper is totally divided into seven parts to go on.In the first part, we review the existing analytical methods in stock market, introduce the definition and developing course of technical analysis and basic situation analysis. We set forth the methods which have been used by the actual technical analysts in stock market and academicians who engaged in related financial theory research. Finally, we put forward the main research way in this paper.In the second part, we introduce two kinds of continuous models, i.e. Black-Scholes Model and stochastic volatility model, which can be used to describe stock price behavior and are popular in financial mathematics. We introduce the development background of these models and give the concrete formula expression in this paper.In the third part, several technical analysis indicators (BOLL, RSI, ROC) are introduced, including the definitions and the applied rules in guiding bargain. We adopt three important stocks in American stock market (DIA, QQQQ, SPY), and give the statistical result in their technical analysis data.In the fourth part, based on the Black-Scholes model, we show some properties of the stochastic processes drawn from the technical analysis indicators. The related laws of large numbers are also discussed.In the fifth part, based on the stochastic volatility model, we provide the definition and related law of large numbers of one kind of asymptotic stationary process when some conditions satisfied. Some properties of the stochastic processes drawn from the technical analysis indicators are also discussed.In the sixth part, we give the distributional histogram plots of a series of stationary processes based on the Black-Scholes model. The corresponding distributional histogram plots of actual data are also shown.And in the last part, we do some tests on stock price model. We reject the hypothesis that stock price follows exponential Levy process. Moreover, we list some problem unsolved in our research.更多还原