【作者】 郭卫娟；

【导师】 刘小茂；

【作者基本信息】 华中科技大学 ， 概率论与数理统计， 2005， 硕士

【摘要】 以风险价值VaR 为核心的风险管理技术是近年来广泛应用的风险评估和计量的数学的模型。对于股票而言,通常假设其收益服从正态分布,在此假设下,关键就是如何估计股票收益分布的均值和方差。就目前的研究情况来看,正态假设下计算风险价值VaR 的方法主要有两种。一种是ARCH / GARCH方法,但ARCH / GARCH模型的一个显著缺点就是只依据最新的样本收益数据去推断均值方差而完全忽略历史样本收益对未来均值方差的影响。另一种是均值或方差的加权计算方法,这类方法的基本原理是对所有的收益数据依照时间次序来分组计算样本均值方差,然后对各组样本均值方差进行简单的固定权数的加权平均,其主要缺点是权数是固定的而不是随最新观测数据而相应变动的随机权数,因而其预测精度也不是很高。为了克服这两类估计方法的缺点,同时又考虑到在实际金融环境中,股票的收益是随着不断变化发展的市场因素而变化的,因此在确定收益分布时既要依据该股票历史收益数据(先验信息),同时也要依据新近数据来估计未来的收益分布,这同时也干反应出股票经营既具有连续性又有变化性。所以本文提出——均值方差变点参数模型,再运用该模型计算深圳A股的风险价值,并介绍模型检验的方法。该方法综合考虑历史收益数据和新近观察数据,在此基础上估计当前时刻的参数值,然后再来计算该股票收益的风险价值。同时,为了检验该模型的合理性,还介绍了检验股票收益序列是否存在变点的三种非参数检验方法,即L-检验法、B -检验法、R-检验法。从理论上讲,这是一种直接检验均值方差变点参数模型的方法; 此外还介绍了两种从风险价值是否合理角度检验均值方差变点参数模型的间接检验方法——F?检验法和泊松检验法,最后指出均值方差变点参数模型中可改进的地方及几个有待思考的问题。更多还原

【Abstract】 Value-at-Risk as the core of risk management has been widely used in many ways such as measuring risk and estimating risk. When it was introduced in measuring the stocks risk, we usually follow the assumption that the stocks return has a Normal distribution. On the assumption the key problem to compute Value-at-Risk is how to estimate the mean and variance of a certain stock. At present, on the Normal distribution, there are two main methods to estimate Value-at-Risk .One is ARCH /GARCH method, but the sort of those method has an obvious shortcoming is that these models based on the merely recent return data which have neglect the experience data. The other method is variety kinds of weighted mean and variance models. The basic principle of this kind of method is to divide all those data into several groups, then reckon mean and variance of each group and make the general estimated mean and variance is formed by the mean of mean and variance of each group. The main shortcoming of these method is which only weighed by simple sample mean and sample variance, which method is not involving any advanced statistics techniques, so the method can not give an estimation with high precision. In order to get over those disadvantages, at the same time, we take into account the reality of that the stocks return is changing over time, so when estimating stocks return we should use both the recent data and the experienced data, which is also determined by the character of stocks management has continuity and variability. So a new model named change-point model of mean and variance was introduce in this papers. We use the very model to calculate the Value-at-Risk of Shenzhen A stock, then we give corresponding knowledge of model test. The method of change-point model of mean and variance can give the real time estimation of mean and variance on the base of the recent data and the experienced data. Since the stocks return is known, we calculate Value-at-Risk of the stocks based on change-point model of mean and variance. At the same time, in order to show the rationality of our model, we introduce three ways of testing for this model: they are L -Test, B -Test, R -test and they all belong to the class of direct test method; moreover ,we also introduce two ways of indirectly testing: F ?Test and Possion Test. Finally we point out some improvability and considerable issue of our model.更多还原