【作者】 魏宇；

【导师】 黄登仕；

【作者基本信息】 西南交通大学 ， 管理科学与工程， 2004， 博士

【摘要】 现代金融风险管理理论和方法(如VaR模型等)以及其它许多经典的金融理论和模型(如CAPM、Black—Scheoles期权定价理论等)都是建立在Fama的“有效市场假说”(Efficient Market Hypothesis, EMH)基础之上的。然而，20世纪70年代以后世界金融市场出现了许多EMH无法解释的“异常现象”(Anomalies)。于是，在20世纪80年代后期兴起的“行为金融学”(Behavioral Finance)和20世纪90年代中后期兴起的“经济物理学”(Econophysics)，或者也有人称之为“物理金融学”(Phynance)的研究正逐渐成为金融市场理论研究的前沿和热点。本文所开展的金融市场的多标度分形(Multifractal)分析也正是“经济物理学”研究中的一个非常重要和前沿的研究领域。近年来的许多国内外实证研究表明，金融市场的时间序列，如汇率、股票价格及其收益率等的波动除了存在混沌(Chaos)和分形(Fractal)等非线性特征之外，还普遍具有明显的多标度分形特征。虽然从理论上讲，通过对金融市场的多标度分形研究，可以得到许多有关金融资产价格在不同时间标度上的不同幅度(特别是极端情况下)的波动信息，可以为我们探究金融市场的复杂性开辟一个崭新的天地。但是，目前绝大多数的相关研究仅仅还停留在对市场价格波动的多标度分形特征的实证检验上，还无法进一步从多标度分形分析中提炼出具有实际可操作性的金融管理决策支持信息。另外，我们知道，有关金融市场在不同时间标度上的不同幅度(特别是极端情况下)的波动信息正是金融风险管理所必需的，因此，本文在“金融市场并非有效市场”的理论假设基础之上，借鉴“经济物理学”的研究方法，首次提出了在金融风险管理中引入多标度分形理论和方法的全新风险管理研究思路，并沿着这一思路建立了基于多标度分形理论的新的风险测度指标和风险预测模型。具体研究内容如下： 1．概述了金融学的发展历史，总结了现代金融学，主要是“有效市场假说”以及现代风险管理理论所面临的困难和挑战；综述了“经济物理学”的产生和发展历程以及最新的研究成果；指出了多标度分形理论在金融学研究中运用的不足及其前景展望。 2．实证研究了中国股票市场这一新兴资本市场的种种异常现象，主要包括中国股票市场价格波动的自相关性特征、持久性特征以及收益率的胖尾分布特征等；发现了沪、深股指恢复正态分布假设的特征时间标度；研究了沪、西南交通大学博士研究生学位论文第n页深股市交易日内的价格波动特征:分析了沪、深股市高频价格数据波动的可预测性。 3.概述了与金融市场研究有关的分形及多标度分形理论;考察了经济系统中的多标度分形现象，并实证研究了中国股票市场的多标度分形特征。 4.提出了在风险管理中引入多标度分形理论和方法的全新风险管理研究思路，并实证检验了这一研究思路的可行性。 5.建立了基于多标度分形谱的全新风险测度指标，验证了其有效性，建立了基于该风险测度指标的价格波动预测模型，并就该指标对价格波动的预测作用进行了实证检验和理论解释。 6.在论文前面的研究基础上，进一步明确提出了应该在金融风险管理研究中引入非线性和复杂性科学理论以及行为金融理论及其研究方法的开放型风险管理研究思路。更多还原

【Abstract】 Modern financial risk management, e.g. VaR model, and many other classical financial theories and models, such as CAPM and Black-Scheoles option pricing theory, are based on Fama’s Efficient Market Hypothesis (EMH). However, many anomalies have been found in world financial markets since 1970s. Therefore, Behavioral Finance, which is risen in the later 1980s, and Econophysics or Phynance, which is risen in the later 1990s, are becoming the front line and hotspot of financial theories. Multifractal analysis of financial markets, which is adopted in this paper, is just one of the most important fields in econophysics. Recently, many empirical studies worldwide have demonstrated that the fluctuations of financial time series, such as exchange rates, stock prices and its returns, show not only chaos and fractal features but also obvious multifractal characteristics. In theories, one may obtain much information about price fluctuations at different times scales with different magnitudes, especially the extreme fluctuations by multifractal analysis of financial markets, which may break a new path in the researches of financial complexity. However, most relative researches by now only focus on the demonstrations of the multifractal characteristics of financial markets, and no further practical decision-supporting information can be obtained from such multifractal analysis. Furthermore, it is well known that information about price fluctuations at different time scales with different magnitudes, especially the extreme fluctuations is imperative in financial risk management. Therefore, based on the hypothesis that financial market is not efficient but fractal and according to the research methods of econophysics, we firstly put forward a new idea that multifractal theories and tools can play important role in the studies of financial risk management. Then we establish a new risk measurement and a risk prediction model based on multifractal theories. The main research contents are as follows:1. The development history of finance, the difficulties and challenges faced by modem finance theories and risk management methods are summarized. The birth, development and the latest fruit of econophysics are also summarized. The prospects of applications of multifractal theories into financial researches are also put forward.2. Many anomalies in Chinese stock markets are empirically studied, such as the autocorrelation, persistence of price fluctuations and fat tailed return distributions, etc. The characteristic time scales of stock indices to recover to normal distribution in Chinese stock market are found. The intraday price volatility and the predictability of high-frequency price fluctuations in Chinese stock market are also studied.3. Fractal and multifractal theories relative to financial markets are summarized. The multifractal phenomenon in economic systems is investigated, and the multifractal characteristic of Chinese stock market is also empirically studied.4. A new idea that the multifractal theories and tools can play important role in the studies of financial risk management are firstly put forward, and its feasibility is also tested.5. Then a new risk measurement and a risk prediction model based on multifractal theories are established, and their validities are also testified.6. Based on the contents studied above, a further research idea that nonlinear, complexity science and behavioral finance theories must be introduced in new financial risk management theories and models.更多还原