基于IS的VaR与CVaR计算与实证分析

发布时间：2018-03-01 04:26

本文关键词： VaR CVaR ARMA模型 Monte Carlo模拟方差缩减技术重要抽样法　出处：《广西师范大学》2014年硕士论文　论文类型：学位论文

【摘要】：VaR(在险价值)和CVaR(条件风险价值)理论是当今社会上在识别、度量和分析风险领域发展得比较成熟的理论,在世界范围内都得到了广泛的运用。但Artzner指出VaR不满足次可加性,不是一致风险估计量,且对风险变量尾部损失的测量不够充分,这导致它往往忽略了对超出阈值的实际发生值的分析。从统计学的角度看,VaR只是一个对应于某置信水平的分位数,没有考察分位点下方的信息,无法精确的刻画出风险。而CVaR满足次可加性,是一致性风险度量,比VaR能更全面地刻画损失分布的特征,对于VaR模型存在的两个缺陷CVaR模型都一一克服了。但Heyde等研究者指出CVaR的这个优点也导致了模型缺乏稳健性。故本文将两者综合在一起分析以促进优势互补。为了提高VaR与CVaR模型度量风险的准确性,国内外众多研究者都围绕着未来金融市场变量的分布、波动率的估计、模型的计算方法等方面进行了大量的研究。在金融市场变量的分布方面,研究者们提出了用几何布朗运动、ARMA模型、广义误差分布、偏斜T分布等来拟合变量的变动过程；在波动率的估计的估计方面,一些研究者发展了ARCH模型、GARCH模型以及ARMA-GARCH模型来捕捉波动信息,解决波动的集聚性问题；在模型的计算方法上,研究者的研究方法主要有：分析法、历史模拟法、蒙特卡洛模拟法等等。然而金融市场风险特别是金融危机的发生是一种稀有事件,要对稀有事件进行计算需要大量的样本量作为保证,这就增加了问题的复杂程度,但上述三种方法都没能解决估计稀有事件存在的问题,这就有待研究者们进一步的修正和改进。相对于传统方法,重要抽样法能够在抽样时分配给引起事件发生的主要原因更大的权重,更利于捕捉稀有事件的发生,进而能提高估计效率。因此,重要抽样技术可以很好的解决这一问题。本文尝试将这种方差缩减技术——重要抽样运用到蒙特卡洛法中,通过指数变换来改变变量的概率测度,使得小概率内包含更多的有效样本以提高模拟效率。本文我们选择ARMA模型作为拟合股票组合日收益率的随机过程,再根据历史数据(或初始值)利用计算机来模拟生成目标时刻的随机数,然后分别采用传统的蒙特卡洛模拟法与基于重要抽样的蒙特卡洛模拟法求得股票组合的VaR与CVaR值,并将计算结果作比较,发现随着置信水平的增大,改进后的蒙特卡洛模拟法的计算结果比传统的蒙特卡洛模拟法的结果更接近于真值,显示出重要抽样法估计稀有事件的有效性。
[Abstract]:The theory of VaR and Cvar (conditional risk value) is a mature theory in the field of identifying, measuring and analyzing risks, which has been widely used all over the world. But Artzner points out that VaR is not satisfied with subadditivity. Not consistent risk estimates, and inadequate measurement of tail loss of risk variables, From a statistical point of view, VaR is just a quantile corresponding to a certain confidence level, without looking at the information below the locus. CVaR satisfies subadditivity, which is a consistent risk measure, which can describe the characteristics of loss distribution more comprehensively than VaR. For the two defects of VaR model, the CVaR model has been overcome one by one. However, Heyde et al. pointed out that this advantage of CVaR also leads to the lack of robustness of the model. Therefore, this paper combines the two models together to promote the complementary advantages. In order to improve the accuracy of risk measurement by VaR and CVaR models, many researchers at home and abroad are focusing on the distribution of variables and the estimation of volatility in the future financial markets. In the aspect of the distribution of financial market variables, the researchers put forward the geometric Brownian motion ARMA model, generalized error distribution and skew T distribution to fit the variation process of the variables. In the estimation of volatility, some researchers have developed ARCH model and ARMA-GARCH model to capture fluctuation information and solve the problem of volatility agglomeration. Historical simulation, Monte Carlo simulation and so on. However, financial market risk, especially the occurrence of financial crisis, is a rare event, to calculate rare events needs a large number of samples as a guarantee. This adds to the complexity of the problem, but none of these three methods can solve the problem of estimating rare events, which requires further revision and improvement by researchers. The important sampling method can assign more weight to the main cause of the event, which is more favorable to capture the rare events, and thus improve the efficiency of estimation. The important sampling technique can solve this problem very well. This paper tries to apply this variance reduction technique to Monte Carlo method to change the probability measure of variables by exponential transformation. Make small probability contain more valid samples to improve the efficiency of simulation. In this paper, we choose ARMA model as a stochastic process to fit the daily return rate of stock portfolio, and then use computer to simulate and generate random number of target time according to historical data (or initial value). Then, the traditional Monte Carlo simulation method and the Monte Carlo simulation method based on important sampling are used to obtain the VaR and CVaR values of the stock combination, and the calculated results are compared, and it is found that with the increase of confidence level, The result of the improved Monte Carlo simulation method is closer to the true value than that of the traditional Monte Carlo simulation method, which shows the effectiveness of the important sampling method in estimating rare events.
【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】：F830.91;O212.2

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