基于拟蒙特卡罗方法的VaR计算及其在中国股市中的实证研究
发布时间：2018-11-11 08:11
【摘要】：随着全球金融市场的蓬勃发展,新的金融产品和金融业务不断出现。与此同时,存在于经济、社会和政治等各方面风险因素也在显著增加,各个类型的金融机构都面临着更多的系统性和非系统性风险。百年难得一遇的全球金融危机更是加剧了人们对于金融风险的担忧,削弱了普通民众对于金融稳定的信心。作为金融风险的管理者和承担者,为了获取相应的超额收益,金融机构不可能完全规避风险,只能从风险的识别、计量、检测和控制上进行提高和改进,尽量减少不惜要的损失。在这种背景下,VaR作为一种测度资产组合在一定概率下最大损失值的方法,得到了越来越多的应用 计算VaR的传统方法包括分析法(方差-协方差法)、历史模拟法和蒙特卡罗模拟法。作为一种全值估计法,蒙特卡罗模拟法计算VaR的应用范围十分广泛,可以适用于非线性资产组合、非正态随机分布和多维风险因子等比较复杂的就算中。但是,蒙特卡罗模拟法也存在着一些较为明显的缺陷,如收敛速率过低和“伪随机数”现象。这些缺陷不仅增大了蒙特卡罗方法的计算量,同时也降低了VaR计算的准确性。因此,本文试图引入拟蒙特卡罗方法对其进行改进。拟蒙特卡罗方法又被称为低差异序列方法。 在文章中,我们构建了拟蒙特卡罗方法计算VaR的基本步骤,并以上证指数为例,在一般误差分布对其进行拟合的基础上,对其收敛性和准确性进行了实证研究。通过实证研究,我们得到了如下结论：1、股票市场收益率的分布规律具有尖峰厚尾的特征,一般误差分布可以很好地拟合股票市场收益率的概率密度分布函数；2、在计算VaR的过程中,相比较于蒙特卡罗方法,拟蒙特卡罗方法具有较快的收敛速率；3、将VaR计算中的蒙特卡罗模拟法替换为拟蒙特卡罗模拟法后,VaR计算的准确性有了明显的提高。拟蒙特卡罗方法在所有的置信水平下都可以通过失败频率检验法的准确性检验。
[Abstract]:With the vigorous development of the global financial market, new financial products and financial business are emerging. At the same time, the risk factors in economic, social and political aspects are also increasing significantly, and various types of financial institutions are facing more systemic and non-systemic risks. The once-in-a-century global financial crisis has exacerbated fears of financial risk and weakened the confidence of ordinary people in financial stability. As financial risk managers and stakeholders, in order to obtain the corresponding excess returns, financial institutions can not completely avoid risk, can only from the risk identification, measurement, detection and control to improve and improve. Try to minimize the losses at your expense. In this context, VaR, as a method to measure the maximum loss value of portfolio under certain probability, has obtained more and more traditional methods to calculate VaR, which include the analysis method (variance-covariance method). Historical simulation and Monte Carlo simulation. As a full value estimation method, Monte Carlo simulation method is widely used to calculate VaR, which can be used in complex cases such as nonlinear portfolio, non-normal random distribution and multi-dimensional risk factors. However, Monte Carlo simulation method also has some obvious defects, such as low convergence rate and "pseudorandom number" phenomenon. These defects not only increase the computational complexity of Monte Carlo method, but also reduce the accuracy of VaR calculation. Therefore, this paper attempts to introduce the quasi-Monte Carlo method to improve it. Quasi-Monte Carlo method is also called low-difference sequence method. In this paper, we construct the basic steps of quasi Monte Carlo method to calculate VaR, and take the Shanghai Stock Exchange Index as an example to study its convergence and accuracy on the basis of general error distribution fitting. Through the empirical research, we get the following conclusions: 1, the distribution law of the stock market yield has the characteristic of sharp peak and thick tail, the general error distribution can fit the probability density distribution function of the stock market rate of return well; 2. In the process of calculating VaR, compared with Monte Carlo method, the quasi-Monte Carlo method has a faster convergence rate. 3. After replacing Monte Carlo simulation method in VaR calculation with quasi Monte Carlo simulation method, the accuracy of VaR calculation is improved obviously. The quasi-Monte Carlo method can pass the accuracy test of failure frequency test at all confidence levels.
【学位授予单位】：复旦大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F224;F832.51
本文编号：2324275
[Abstract]:With the vigorous development of the global financial market, new financial products and financial business are emerging. At the same time, the risk factors in economic, social and political aspects are also increasing significantly, and various types of financial institutions are facing more systemic and non-systemic risks. The once-in-a-century global financial crisis has exacerbated fears of financial risk and weakened the confidence of ordinary people in financial stability. As financial risk managers and stakeholders, in order to obtain the corresponding excess returns, financial institutions can not completely avoid risk, can only from the risk identification, measurement, detection and control to improve and improve. Try to minimize the losses at your expense. In this context, VaR, as a method to measure the maximum loss value of portfolio under certain probability, has obtained more and more traditional methods to calculate VaR, which include the analysis method (variance-covariance method). Historical simulation and Monte Carlo simulation. As a full value estimation method, Monte Carlo simulation method is widely used to calculate VaR, which can be used in complex cases such as nonlinear portfolio, non-normal random distribution and multi-dimensional risk factors. However, Monte Carlo simulation method also has some obvious defects, such as low convergence rate and "pseudorandom number" phenomenon. These defects not only increase the computational complexity of Monte Carlo method, but also reduce the accuracy of VaR calculation. Therefore, this paper attempts to introduce the quasi-Monte Carlo method to improve it. Quasi-Monte Carlo method is also called low-difference sequence method. In this paper, we construct the basic steps of quasi Monte Carlo method to calculate VaR, and take the Shanghai Stock Exchange Index as an example to study its convergence and accuracy on the basis of general error distribution fitting. Through the empirical research, we get the following conclusions: 1, the distribution law of the stock market yield has the characteristic of sharp peak and thick tail, the general error distribution can fit the probability density distribution function of the stock market rate of return well; 2. In the process of calculating VaR, compared with Monte Carlo method, the quasi-Monte Carlo method has a faster convergence rate. 3. After replacing Monte Carlo simulation method in VaR calculation with quasi Monte Carlo simulation method, the accuracy of VaR calculation is improved obviously. The quasi-Monte Carlo method can pass the accuracy test of failure frequency test at all confidence levels.
【学位授予单位】：复旦大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F224;F832.51
【参考文献】
相关期刊论文 前2条
1 汪东,张为黎;使用拟蒙特卡罗模拟的欧式看涨期权的定价[J];生产力研究;2004年07期
2 傅强;邢琳琳;;基于极值理论和Copula函数的条件VaR计算[J];系统工程学报;2009年05期
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