基于混合分布的VaR估计及其应用

发布时间：2018-01-07 21:03

本文关键词：基于混合分布的VaR估计及其应用　出处：《电子科技大学》2015年硕士论文　论文类型：学位论文

【摘要】：随着金融衍生品的丰富和信息技术的发展,金融市场的交易范围与交易速度大大提升,金融产品种类也大大增加。金融市场的交易量快速增加,不同地区金融市场间的关联性不断增强。当金融风险事件发生时,会迅速传播影响到关联地区,重则引发多国性的区域金融危机。历史上的多次大规模金融危机印证了这一点,因此金融管理机构越来越重视金融风险管理。《巴塞尔协议》1996年修正案引入在险价值VaR(Value at Risk)这一概念,来对银行资本金的风险进行度量。此后VaR得到了广泛的应用,成为通用的风险度量指标。现有的VaR估计方法主要分为三类:参数方法,主要为各类GARCH族模型;半参数方法,主要为基于极值理论的估计方法;非参数方法,主要包括历史模拟法、蒙特卡洛法等。现有的VaR估计方法基本都假定收益率分布为单一分布,如传统的正态分布、t分布等,而非混合分布。相较单一分布,混合分布拥有多个子分布,能够更为灵活地生成非对称分布与厚尾分布,更准确地刻画金融收益率的非对称特征与高峰厚尾特征。本文将收益率分布假定为混合分布,提出了一种基于混合分布的VaR非参数估计方法及参数化的NM-GARCH-POT模型。在基于混合分布的VaR非参数估计方法中,假定不同市场行情下的收益率服从不同的子分布,通过检验日内收盘价序列的平稳性来对子分布进行分类。使用基于Bootstrap的核密度估计方法估计子分布的概率密度。最后利用子分布概率密度函数与子分布出现概率,使用蒙特卡洛模拟法得到总体分布的VaR估计值。根据子分布出现概率是否为条件概率的不同,分别构建了无条件混合分布模型(u-MD)与条件混合分布模型(c-MD)。实证结果表明u-MD模型与c-MD模型都是有效的VaR估计模型,相较GARCH族模型有更好的空头估计效果,在不同数据上有更稳定的估计表现。参数化的NM-GARCH-POT模型假定随机扰动项服从有两个子分布的混合正态分布。首先使用NM-GARCH模型对收益率序列进行建模,估计收益率样本的条件均值与条件方差并计算得到标准化残差。然后使用POT模型对标准化残差建模,估计出标准化残差的分位数。最后通过公式计算得到收益率的VaR。实证结果表明NM-GARCH-POT模型能够准确地表述收益率分布尾部,是一种有效的VaR估计方法。
[Abstract]:With the development of financial derivatives and rich information technology, transaction scope and financial market transaction speed is greatly improved, the variety of financial products has greatly increased. The rapid increase in the trading volume of the financial market, the financial markets association between different regions is growing. When the financial risk event occurs, will affect the rapid spread of related areas, heavy it triggered the financial crisis in the history of the region. Many large-scale financial crisis proved this point, so the financial management institutions should pay more attention to financial risk management. The Basel accord >1996 amendment into the value at risk VaR (Value at Risk) this concept, to the risk of Bank capital measurement. Since the VaR has been widely used as a general risk measurement index. The existing VaR estimation method is mainly divided into three categories: parametric methods, mainly for all types of semi parametric GARCH models; The main method for estimation method based on extreme value theory; non parametric methods, including historical simulation method, Monte Carlo method. The existing VaR estimation method basically assumes that the rate of return distribution for a single distribution, such as the traditional normal distribution, t distribution, and non mixed distribution. Compared with the single phase distribution, with mixed distribution the sub distribution can be more flexible to generate asymmetric distribution and heavy tailed distribution, more accurately describe the characteristics of asymmetric features with high peak and thick tail of the financial rate of return. The rate of return distribution is assumed for the mixed distribution, based on the mixed VaR distribution NM-GARCH-POT model method and non parametric parameters estimated. In the non parameter estimation method in mixed distribution based on the VaR assumption in different market conditions yields obey different sub distribution, through the stationary test days closing price series to sub distribution points Use the Bootstrap class. The kernel density estimation method to estimate the probability density distribution. Finally based on the sub sub distribution probability density function and probability distribution, using Monte Carlo simulation method to obtain the overall distribution of VaR estimates. According to the distribution of probability is a conditional probability, respectively established the unconditional mixture distribution model (u-MD) and conditions of mixed distribution model (c-MD). The empirical results show that the u-MD model and c-MD model are effective VaR estimation model, compared with the GARCH model has a better estimation effect is short, estimation performance is more stable in different data. We assume that the random perturbation obey mixed two sub distribution of normal distribution of NM-GARCH-POT model parametric. First use the NM-GARCH model of the return series, and the estimation of the conditional mean conditional yield variance of sample and calculate the standard residuals Then, we use POT model to model standardized residuals, estimate the quantile residuals of standardized residuals. Finally, we get the VaR. rate of return through formula calculation. The empirical results show that NM-GARCH-POT model can accurately represent the tail of yield distribution, and it is an effective VaR estimation method.

【学位授予单位】：电子科技大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：F224

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