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1、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序来分组计算样本均值方差这类方法的基本原理是对所有的收益数据依照时间次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
2、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
3、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考的问题关键词 风险价值 VaR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均值方差变点参数模型 贝叶斯方法 条件分布 假设检验非参数检验F 检验泊松检验IAbstractsValue-at-Riskas the core of risk management has been widely used in many wayssuch as measuring risk and estimating risk. When
4、 it was introduced in measuring the stocksrisk, we usually follow the assumption that the stocks return has a Normal distribution. Onthe assumption the key problem to compute Value-at-Risk is how to estimate the mean andvariance of a certain stock.At present, on the Normal distribution, there are tw
5、o main methods to estimateValue-at-Risk .One is ARCH / GARCH method, but the sort of those method has anobvious shortcoming is that these models based on the merely recent return data which haveneglect the experience data. The other method is variety kinds of weighted mean andvariance models. The ba
6、sic principle of this kind of method is to divide all those data intoseveral groups, then reckon mean and variance of each group and make the generalestimated 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 simp
7、le sample mean andsample variance, which method is not involving any advanced statistics techniques, so themethod can not give an estimation with high precision. In order to get over thosedisadvantages, at the same time, we take into account the reality of that the stocks return ischanging over time
8、, so when estimating stocks return we should use both the recent data andthe experienced data, which is also determined by the character of stocks management hascontinuity and variability. So a new model named change-point model of mean and variancewas introduce in this papers. We use the very model
9、 to calculate the Value-at-Risk ofShenzhen A stock, then we give corresponding knowledge of model test. The method ofchange-point model of mean and variance can give the real time estimation of mean andvariance on the base of the recent data and the experienced data. Since the stocks return isknown,
10、 we calculate Value-at-Risk of the stocks based on change-point model of mean andvariance. At the same time, in order to show the rationality of our model, we introducethree ways of testing for this model: they are L Test, B Test, R test and they all belongIIto the class of direct test method; moreo
11、ver ,we also introduce two ways of indirectly testing:F Test and Possion Test. Finally we point out some improvability and considerable issueof our model.Key words: Value-at-Risk; the change-point model of mean and variance; bayes method;Conditional distribution; hypothesis test; non-parameter hypot
12、hesis test; F Test ;Possion TestIII独创性声明本人声明所呈交的学位论文是我个人在导师的指导下进行的研究工作及取得的研究成果近我所知 除文中已标明引用的内容外 本论文不包含任何其他人或集体已经发表或撰写过的研究成果 对本文的研究做出贡献的个人和集体 均已在文中以明确方式标明 本人完全意识到本声明的法律结果由本人承担学位论文作者签名 郭卫娟日期 2005 年 5 月 8 日学位论文版权使用授权书本学位论文作者完全了解学校有关保留使用学位论文的规定 即学校有权保留并向国家有关部门或机构送交论文的复印件和电子版 允许论文被查阅和借阅 本人授权华中科技大学可以将本学位论文的全部或部分内容编入有关数据库进行检索 可以采用影印 缩印或扫描等复制手段保存和汇编本学位论文保密本论文属于不保密请在以上方框内打在_年解密后适用本授权数学位论文作者签名郭卫娟指导教师签名 刘小茂日期 2004 年 5 月 8 日日期 2004 年 5 月 8 日1 绪 论随着金融市场规模的不断扩大以及金融市场风波导致的巨大损失的不断发生使得金融监管层开始重新研究有效的风险管理工具 1993 年一个由工业国家的高层银行
