CVaR和CES的局部线性估计的模拟研究与实证分析
发布时间:2018-01-02 05:25
本文关键词:CVaR和CES的局部线性估计的模拟研究与实证分析 出处:《广西师范大学》2014年硕士论文 论文类型:学位论文
【摘要】:随着经济全球化的进程加快,人们逐渐意识到在获得更大的机遇的同时,风险必然随之加剧。于是乎,越来越多的人们开始重视这个问题——如何度量甚至是控制风险?国内外,许多的学者开始了这方面的研究,1994年,Morgan投资银行在"Risk metrics"的系统中最早提出VaR技术,因为它具有的多方面的优势,慢慢的被大家所接受,到目前为止,VaR方法作为一种国际性经融风险管控指标,成为了更多企业必不可少的风险管理工具。 风险价值VaR是一种重要的金融风险度量指标,近期有很多关于动态VaR以及条件VaR(CVaR)等方面的研究。本文介绍了国内外对VaR的研究,以及CVaR对VaR的改进,随后介绍了三种选择窗宽的方法:Silverman的大拇指法则、极大光滑原则和交叉验证法。提出用一种新的非参数估计--局部线性估计对条件风险价值CVaR和期望损失ES(expected shortfall)进行估计,并与N-W估计进行对比,对比不同方法不同估计值与真值之间的误差,发现局部线性估计优于N-W核估计。在模拟研究中,通过Silverman大拇指法则选择窗宽,用R软件编写程序,进行随机数生成样本,计算CVaR和CES的估计值,用列表展现出不同的置信水平P值和X的情况下,CVaR和CES的变化。最后,在实证研究中,选取上证指数和沪深300指数数据(样本期为2010年3月29日~2011年1月20日)为研究对象,先用ADF检验序列,发现上证指数序列和沪深300指数序列一阶差分后的序列不存在单位根,所以该序列都是一阶单整序列。 最后,用局部线性估计的方法计算了股票市场数据所隐含的CVaR和CES.无论是沪深300指数,还是上证指数,利用非参数局部线性估计估计得到的风险波动函数,都呈现U型,即所谓的“波动率微笑”现象,这可以看成是一种变异风险度量,有着随r波动的特性,容易分析并且直观。对于缺乏概率统计相关知识的一般投资者来说,所使用的风险度量指标——标准差的概念,分析起来并不直观,也不容易被解释、认同。无论是CVaR或者CES,估计值的图形都呈现U型,正好对应于所谓的“波动率微笑”。当风险倾向降低,上证指数的滞后损失值将会慢慢趋向于经验平均值。这些结果对股票市场风险评价有一定的参考价值。
[Abstract]:With the acceleration of the process of economic globalization, people are gradually realizing that while getting more opportunities, the risks will inevitably increase. More and more people are beginning to pay attention to this question-how to measure and even control risk? At home and abroad, many scholars began to study this aspect. In 1994, Morgan Investment Bank first put forward VaR technology in the system of "Risk metrics". Because it has many advantages, gradually accepted by everyone, so far VaR method as an international financial risk management index, has become an essential risk management tool for more enterprises. Value of risk (VaR) is an important measure of financial risk. Recently, there are many researches on dynamic VaR and conditional VaR Cvar. This paper introduces the research of VaR at home and abroad, and the improvement of VaR by CVaR. Then three methods of selecting window width: Silverman's thumb rule are introduced. Maximum smoothness principle and cross validation method. A new nonparametric estimator, local linear estimator, is proposed for conditional risk value (CVaR) and expected loss ES( s). Expected shortfall. By comparing with N-W estimation and comparing the error between different estimators and true values of different methods, it is found that local linear estimation is better than N-W kernel estimation. The window width is selected by the Silverman thumb rule, and the program is written with R software. The samples are generated by random numbers, and the estimated values of CVaR and CES are calculated. Show the change of Cvar and CES in the case of P and X with different confidence levels. Finally, in the empirical study. The data of Shanghai Stock Exchange Index and Shanghai and Shenzhen 300 Index (sample period from March 29th 2010 to January 20th 2011) were selected as the research object, and the ADF test sequence was used first. It is found that there is no unit root in the sequence after the first order difference between the Shanghai stock index sequence and the Shanghai and Shenzhen 300 index sequence, so the sequence is single integer sequence of the first order. Finally, the implicit CVaR and CESs of stock market data are calculated by using the method of local linear estimation, whether the CSI 300 index or the Shanghai Stock Exchange index. All the risk fluctuation functions obtained by using non-parametric local linear estimators are U-shaped, that is, the so-called "volatility smile" phenomenon, which can be regarded as a variation risk measure with the characteristic of fluctuation with r. It is easy to analyze and intuitionistic. For the general investors who lack the relevant knowledge of probability and statistics, the concept of standard deviation, which is used as a risk measure, is not intuitively analyzed and can not be easily explained. Agree. Regardless of whether it is CVaR or CES, the figure of the estimate is U-shaped, which corresponds to the so-called "volatility smile." when the risk propensity decreases. The lag loss value of Shanghai Stock Exchange Index will gradually tend to the empirical average. These results have certain reference value for stock market risk evaluation.
【学位授予单位】:广西师范大学
【学位级别】:硕士
【学位授予年份】:2014
【分类号】:O212.7;F830.91
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