本文關(guān)鍵詞：Copula-MCMC理論在投資組合風(fēng)險管理上的應(yīng)用　出處：《湖南師范大學(xué)》2013年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 投資組合 Copula MCMC 風(fēng)險值

【摘要】：本文對國內(nèi)外關(guān)于投資組合及其風(fēng)險值的研究進(jìn)行了綜述,雖然投資組合理論現(xiàn)已形成了完整的體系,但仍有不足的地方,主要體現(xiàn)在計算組合VaR值基于線性假設(shè)和確定最優(yōu)投資組合的實(shí)際操作比較繁瑣,而用MCMC方法操作起來比較簡單,所以嘗試將Copula理論和MCMC方法結(jié)合運(yùn)用到投資組合分析中,并與傳統(tǒng)的方法進(jìn)行了比較,得出的結(jié)論是Copula-MCMC方法在資產(chǎn)配置和風(fēng)險度量方面具有一定的改善效果。全文主要分為三個部分： 第一部分,對Copula理論和MCMC方法的相關(guān)理論知識進(jìn)行了闡述,有選擇性地介紹了常用的Copula函數(shù),如多元正態(tài)Copula函數(shù)、多元t-Copula函數(shù)和阿基米德Copula函數(shù),并且介紹了M-H算法實(shí)施的具體步驟。 第二部分,建立Copula模型和對計算VaR的方法進(jìn)行改進(jìn),根據(jù)金融資產(chǎn)的波動性特征,用GARCH(1,1)模型來描述其特性,再結(jié)合Copula函數(shù)建立Copula-GARCH(1,1)模型,采用兩階段極大似然法對模型參數(shù)進(jìn)行估計,然后用對數(shù)似然值和AIC值評價模型的擬合優(yōu)度。傳統(tǒng)方法計算VaR值用到的相關(guān)系數(shù)是線性的,而Copula模型中的相關(guān)系數(shù)能夠很好地刻畫金融資產(chǎn)的非線性相關(guān)關(guān)系,因此用Copula模型中的相關(guān)系數(shù)代替線性相關(guān)系數(shù)計算VaR更加符合實(shí)際。再根據(jù)樣本數(shù)據(jù)的先驗(yàn)概率通過MCMC方法確定投資組合資產(chǎn)比例,用該比例和Copula模型相關(guān)系數(shù)計算VaR的值。 第三部分,用建立的模型進(jìn)行實(shí)證分析,本文選擇歐盟排放權(quán)配額期貨合約和華夏全球精選基金作為數(shù)據(jù)樣本,對數(shù)據(jù)用Q-Q圖檢驗(yàn)發(fā)現(xiàn)樣本數(shù)據(jù)的分布近似服從正態(tài)分布,所以選擇用多元正態(tài)Copula函數(shù)作為連接函數(shù)。然后再用樣本數(shù)據(jù)估計GARCH(1,1)模型參數(shù),進(jìn)而估計Copula-GARCH(1,1)模型的相關(guān)系數(shù)。最后分別用改進(jìn)后的方法和傳統(tǒng)方法計算了VaR的值,經(jīng)比較后發(fā)現(xiàn)改進(jìn)后的方法計算出來的VaR稍微比傳統(tǒng)的要高一些,說明傳統(tǒng)方法低估了風(fēng)險,改進(jìn)后的方法更加符合實(shí)際情況。
[Abstract]:This paper summarizes the research on portfolio and its risk value at home and abroad. Although portfolio theory has formed a complete system, but there are still shortcomings. The main manifestation is that the calculation of portfolio VaR value based on linear assumptions and the determination of the optimal portfolio of the actual operation is more cumbersome, but using the MCMC method to operate is relatively simple. So we try to apply Copula theory and MCMC method to portfolio analysis, and compare with traditional methods. The conclusion is that the Copula-MCMC method has a certain improvement effect in asset allocation and risk measurement. In the first part, the related theoretical knowledge of Copula theory and MCMC method is expounded, and the commonly used Copula functions, such as multivariate normal Copula functions, are introduced selectively. The multivariate t-Copula function and Archimedes Copula function are introduced, and the steps of M-H algorithm implementation are introduced. In the second part, the Copula model is established and the method of calculating VaR is improved. According to the volatility characteristics of financial assets, it is described by the Garch 1 / 1) model. Then the Copula-GARCH1) model is established with the Copula function, and the parameters of the model are estimated by using the two-stage maximum likelihood method. Then the logarithmic likelihood value and AIC value are used to evaluate the goodness of fit of the model. The correlation coefficient used in the traditional method to calculate the VaR value is linear. The correlation coefficient in Copula model can well describe the nonlinear correlation of financial assets. Therefore, using correlation coefficient in Copula model instead of linear correlation coefficient to calculate VaR is more practical. Then according to the prior probability of sample data, the ratio of portfolio assets is determined by MCMC method. The ratio and the correlation coefficient of Copula model are used to calculate the value of VaR. In the third part, using the established model for empirical analysis, this paper selects the European Union emissions quota futures contract and the Huaxia Global selection Fund as data samples. The Q-Q graph test shows that the distribution of the sample data is similar to the normal distribution, so the multivariate normal Copula function is chosen as the connection function, and then the sample data is used to estimate the GARCH(1. 1) the parameters of the model and the correlation coefficient of the Copula-GARCH1) model are estimated. Finally, the values of VaR are calculated by the improved method and the traditional method. After comparison, it is found that the VaR calculated by the improved method is slightly higher than that of the traditional one, which indicates that the traditional method underestimates the risk, and the improved method is more in line with the actual situation.
【學(xué)位授予單位】：湖南師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2013
【分類號】：F832.48;F224

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