Copula分布估计算法及其在金融风险分析上的应用研究

发布时间：2018-08-14 13:45

【摘要】：随着近几十年国际上金融行业的发展以及金融市场的变迁,金融资产管理的风险也逐步加剧,因此资产管理配置问题也是近年来学术界研究的热点问题之一。Markowitz(1952)的均值—方差模型为现代的资产组合理论奠定了一定的基础[1]。Copula分布估计算法是结合Copula理论和分布估计算法二者产生的一种智能优化算法。Copula理论,为获取联合分布提供了一种方法,它提出将联合分布分解为一个连续函数和多个边缘分布[2],其中,边缘分布反映单变量变化,函数说明变量间的相关结构。与联合分布相比,获取变量的边缘分布相对更容易,取样更简单。智能优化算法兴起于20世纪30年代,引入了生物进化的思想和特征,主要包括选择、遗传等,典型算法如遗传算法、菌群算法粒子群优化算法等。而分布估计算法是基于遗传算法发展起来的一种进化算法,其主要特点是建立概率模型来得到新个体[3]。分布估计算法在运算时具有高效的优点,但是在估计概率模型时,其操作比较复杂,运算量也比较庞大。因此,本文将Copula理论和分布估计算法结合运用,利用Copula理论的优势简化分布估计算法建立概率分布模型的过程,并将Copula分布估计算法运用到金融风险分析领域进行应用,并且引入菌群算法复制的思想进行改进。然后将Copula-Va R模型计算的结果与Copula分布估计算法度量风险的结果进行对比,说明使用算法的有效性。在算法目标优化函数的选取上,本文引入了风险调整资本收益这一目标函数,更符合风险的实际含义。其次,通过实证说明了Copula函数可以很好的获取到各金融资产之间的有效信息,尤其是金融资产不服从正态分布,具有尖峰厚尾分布特征的特性[2]。投资者在面对当今风险加剧的金融市场时,对于风险分析度量的要求会越来越高,因为投资者会希望以更小的风险达到最大化的收益,更好地进行资产配置。因此本文将Copula分布估计算法应用到风险分析中是有现实意义的,为风险度量提供了又一种方法。
[Abstract]:With the development of the international financial industry and the changes of the financial market in recent decades, the risk of financial asset management has been gradually increased. Therefore, asset management allocation is one of the hot issues in academic circles in recent years. The mean-variance model of Markowitz (1952) has laid a certain foundation for modern portfolio theory [1] .Copula distribution estimation algorithm is based on Copula theory and distribution. Copula theory, an intelligent optimization algorithm produced by both estimation algorithms, In order to obtain the joint distribution, a method is provided in which the joint distribution is decomposed into a continuous function and several edge distributions [2], in which the edge distribution reflects the variation of the single variable, and the function explains the correlation structure between the variables. Compared with the joint distribution, it is easier to obtain the marginal distribution of variables and to sample them more easily. Intelligent optimization algorithm was developed in 1930s. It introduces the idea and characteristics of biological evolution, including selection, heredity, typical algorithms, such as genetic algorithm, bacterial colony algorithm, particle swarm optimization algorithm and so on. The distribution estimation algorithm is an evolutionary algorithm based on genetic algorithm. Its main feature is to establish a probability model to get new individuals. The distributed estimation algorithm has the advantage of high efficiency in operation, but in estimating the probabilistic model, its operation is more complicated, and the computation is very large. Therefore, this paper combines the Copula theory and the distribution estimation algorithm to simplify the process of establishing the probability distribution model by using the advantage of the Copula theory, and applies the Copula distribution estimation algorithm to the field of financial risk analysis. And the idea of replicating bacteria colony algorithm is introduced to improve it. Then the results of Copula-Va R model calculation are compared with the results of Copula distribution estimation algorithm to measure the risk, which shows the effectiveness of using the algorithm. In the selection of the optimization function of the algorithm, this paper introduces the objective function of risk-adjusted capital return, which is more in line with the actual meaning of risk. Secondly, it is proved that the Copula function can obtain the effective information between the financial assets, especially the characteristics of the financial assets with the characteristics of peak and thick tail distribution. In the face of the financial market where the risk is increasing, the demand for risk analysis will be higher and higher, because investors will want to maximize the return with less risk and better asset allocation. Therefore, it is of practical significance to apply Copula distribution estimation algorithm to risk analysis, which provides another method for risk measurement.
【学位授予单位】：广东财经大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：F830;F224

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