基于pair-Copula情景生成的CVaR投资组合模型研究

发布时间：2018-04-15 09:23

本文选题：Copula + GARCH　；参考：《中国科学技术大学》2017年硕士论文

【摘要】：对资产组合的风险描述方法,在最初马科维茨(Markowitz)提出的M-V模型中用资产收益率的方差来描述风险。方差作为描述随机变量离散水平的统计量,包含了随机变量在均值周围的向上和向下波动。后来,研究者提出了 VaR(Value at Risk,在险价值)这一衡量指标。VaR表示资产组合在一定置信水平下,将来一定时间段中可能产生的最大损失值。因此相比较方差而言,VaR更偏重下行风险。但在VaR的计算中,一般情况下会假设资产的收益率分布服从正态分布,这与实际情况有较大差别。因此,运用Copula来描述资产收益率之间的相依关系并找到他们的联合分布是一个很好的方法。在金融资产的配置和资产组合的研究中我们会用到随机优化模型作为分析工具,随机优化模型的整体分析思路是模拟生成资产收益率的情景,同时根据生成的情景构造情景树,将生成的情景树代入模型求解,由此得到优化结果。传统的K-means聚类分析产生收益率的情景在初始需要根据经验人为设定分类的个数K,具有主观性和不确定性,基于对上述K-means聚类分析方法的改进,本文选择使用Copula来描述资产收益率之间的相依关系并得到联合分布,同时用基于Copula的情景生成方法生成的情景构造情景树,并将得到的结果代入模型,得到最优的投资组合。依据上面的思路,本文先介绍了 Copula以及相应的边缘分布建模方法,并介绍了 VaR和CVaR模型来描述风险。随后本文通过GARCH模型对资产收益率的边缘分布建模,并使用Copula得到收益率的联合分布,并由蒙特卡洛模拟生成收益率的情景,得到的结果代入广义熵约束的CVaR模型中,由此得到最优的投资权重。文章随机选取了中国股市中的四只股票构造投资组合并进行实证分析,本文实证表明,在考虑不同资产之间的相依结构基础上得到的最优化结果相比传统的投资组合M-V模型具有明显的优势,在分散化和收益性上得到很好的效果。
[Abstract]:In the original M-V model proposed by Markowitz Markowitz, the risk description method of portfolio is described by variance of return rate of assets.Variance, as a statistic describing the discrete level of random variables, includes the upward and downward fluctuations of random variables around the mean.Later, the researcher put forward the VaR(Value at risk value. VaR indicates the maximum loss value of the portfolio in a certain confidence level and in a certain period of time in the future.Therefore, compared with variance, VaR is more partial to downlink risk.However, in the calculation of VaR, the return distribution of assets is assumed to be normal distribution, which is different from the actual situation.Therefore, it is a good method to use Copula to describe the relationship between asset returns and find their joint distribution.In the research of financial asset allocation and portfolio, we will use stochastic optimization model as an analysis tool. The overall analysis idea of stochastic optimization model is to simulate the situation of generating the return rate of assets, and to construct scenario tree according to the generated scenario at the same time.The generated scenario tree is substituted into the model and the optimization result is obtained.In the traditional K-means clustering analysis, the return rate scenarios need to set the number of categories artificially according to the experience K, which is subjective and uncertain, based on the improvement of the above K-means clustering analysis method.In this paper, we choose to use Copula to describe the dependency relationship between asset returns and obtain the joint distribution. At the same time, scenario tree is constructed by scenario generation method based on Copula, and the result is substituted into the model to obtain the optimal portfolio.According to the above ideas, this paper first introduces the Copula and the corresponding edge distribution modeling method, and introduces the VaR and CVaR models to describe the risk.Then this paper uses GARCH model to model the edge distribution of asset return rate, and uses Copula to obtain the joint distribution of return rate, and the Monte Carlo simulation is used to generate the situation of return rate, and the result is substituted into the generalized entropy constrained CVaR model.Thus the optimal investment weight is obtained.This paper randomly selects four stocks in Chinese stock market to construct a portfolio and makes an empirical analysis.Compared with the traditional portfolio M-V model, the optimization results obtained on the basis of considering the dependent structure of different assets have obvious advantages, and have a good effect on decentralization and profitability.
【学位授予单位】：中国科学技术大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224;F832.51

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