基于M-Copula函数的投资组合和相关风险研究

发布时间：2018-06-19 23:18

本文选题：M-Copula函数 + GJRSK-M模型　；参考：《重庆大学》2014年硕士论文

【摘要】：文中采用EGARCH-M模型进行了单个资产建模，及用M-Copula函数构建了多个资产的联合分布，对基于GED分布的联合资产收益率构建了M-Copula-EGARCH-M模型，并采用Monte Carlo模拟方法计算出不同投资比例和置信水平的组合风险VaR和CVaR的值，并求出不同期望收益和置信水平下的最优组合投资权重。实证结果表明，本文模型有利于投资者对投资权重的选择。同时，由于金融资产不但存在方差风险，还存在时变偏度风险和时变峰度风险，这使得仅从金融资产的前两阶矩出发来研究风险变化显得十分局限。GJRSK-M模型是描述金融资产的高阶矩风险的有效工具，可对单个金融资产的分布进行拟合，而M-Copula函数能连接组合金融资产的边缘分布，因此本文又建立了M-Copula-GJRSK-M模型来研究沪深两股票市场的相依性。实证表明，上证综指和深圳成指对数收益率存在高阶矩风险和风险的非对称性，即指数下跌时，条件方差风险和条件高阶矩风险会增大。本文研究成果如下： ①提出了基于M-Copula-EGARCH-M-GED的投资组合模型。选用能刻画风险溢价的EGARCH-M模型对各单个资产收益率进行建模，选用M-Copula作为联合分布连接函数，，用遗传算法对模型中参数进行计算，用基于GED分布的CVaR度量风险，利用Monte Carlo方法模拟求得不同投资比例和置信水平下的VaR和CVaR值，求出不同期望收益和置信水平下的最优组合投资权重。 ②提出了基于M-Copula-GJRSK-M模型对沪深两市的相依性进行分析。选用GJRSK-M模型刻画资产组合的边缘分布，以反映单个资产价格波动的高阶矩风险的时变性和非对称性，再结合混合Copula函数建立M-Copula-GJRSK-M模型来研究组合资产的相依结构并展开实证研究。 ③根据金融市场投资的联动性和相关性，引入能够囊括各种相关结构变化的三种阿基米德Copula函数,即选用了Gumble、Clayton和Frank Copula函数的线性组合来构造混合Copula函数。由此更为灵活的描述具有复杂相关关系的事物之间的关联度，如金融市场之间的相关关系。 ④采用一个服从2分布的M经验统计量来评价M-Copula函数的拟合度，从而刻画金融市场之间的相关模式；采用Ljung-Box Q检验法和K-S检验法对EGARCH-M模型的残差序列的相关性和误差分布的拟合度进行检验，进而对EGARCH-M合理性进行验证；运用Gram-Charlier以及Leon对其定义式做了修正，利用正态分布展开对GJRSK-M模型进行估计，从而能够更精准的捕捉到尾部分布和峰度的陡缓。 ⑤选取中国证券市场中具有代表性的上证综指和深圳成指，利用统计和数据处理软件，对本文提出模型、方法以及所得结论进行实证分析，实证结论与理论推导结论吻合。
[Abstract]:In this paper, the EGARCH-M model is used to model the individual assets, and the joint distribution of multiple assets is constructed with the M-Copula function. The M-Copula-EGARCH-M model is constructed for the joint asset returns based on the GED distribution, and the Monte Carlo simulation method is used to calculate the value of the combined risk VaR and CVaR of different investment ratios and confidence levels. The empirical results show that the model is beneficial to the investor's choice of investment weight. At the same time, the financial assets not only have variance risk, but also have time variant and time-varying kurtosis risk, which makes the study only from the first two moments of financial assets. The.GJRSK-M model is an effective tool to describe the high moment risk of financial assets. It can fit the distribution of individual financial assets, and the M-Copula function can connect the marginal distribution of the combined financial assets. Therefore, this paper also establishes the M-Copula-GJRSK-M model to study the dependence of the two stock market in Shanghai and Shenzhen. The evidence shows that the high order moment risk and the risk are unsymmetrical in the Shanghai Composite Index and the Shenzhen index logarithm yield rate, that is, when the index falls, the conditional variance risk and the conditional high moment risk will increase.
The results of this study are as follows:
(1) an investment portfolio model based on M-Copula-EGARCH-M-GED is proposed. The EGARCH-M model which can depict the risk premium is used to model the yield of individual assets, M-Copula is selected as the joint distribution function, the parameters in the model are calculated by genetic algorithm, and the CVaR based on the GED distribution is used to measure the risk, and the Monte Carlo method is used. The VaR and CVaR values of different investment ratios and confidence levels are obtained by simulation, and the optimal portfolio weights under different expected returns and confidence levels are obtained.
Secondly, based on M-Copula-GJRSK-M model, the dependence of Shanghai and Shenzhen two cities is analyzed. GJRSK-M model is used to describe the marginal distribution of asset portfolio to reflect the time variability and asymmetry of the high order moment risk of single asset price fluctuation, and then combine the mixed Copula function to establish the M-Copula-GJRSK-M model to study the dependence of the combined assets. The structure and the empirical study are carried out.
(3) based on the linkage and correlation of financial market investment, three kinds of Archimedes Copula functions, which can include all kinds of related structural changes, are introduced to construct a mixed Copula function by using the linear combination of Gumble, Clayton and Frank Copula functions. Such as the relationship between the financial market.
(4) using a M empirical statistic that obeys the 2 distribution to evaluate the fitting degree of the M-Copula function, thus depicts the correlation model between the financial markets, and tests the correlation of the residual sequence of the EGARCH-M model and the fitting degree of the error distribution by the Ljung-Box Q test method and the K-S test method, and then verifies the rationality of the EGARCH-M. Gram-Charlier and Leon are used to modify the definition, and the normal distribution expansion is used to estimate the GJRSK-M model, thus the steepness of the tail distribution and kurtosis can be more accurately captured.
5. Select the Representative Shanghai Composite Index and the Shenzhen index in China's securities market. By using statistics and data processing software, this paper makes an empirical analysis of the models, methods and conclusions, and the empirical conclusions are in agreement with the theoretical conclusions.
【学位授予单位】：重庆大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F832.51;F224

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