本文選題：M-Copula函數(shù) + GJRSK-M模型�。� 參考：《重慶大學(xué)》2014年碩士論文

【摘要】：文中采用EGARCH-M模型進(jìn)行了單個(gè)資產(chǎn)建模，及用M-Copula函數(shù)構(gòu)建了多個(gè)資產(chǎn)的聯(lián)合分布，對基于GED分布的聯(lián)合資產(chǎn)收益率構(gòu)建了M-Copula-EGARCH-M模型，并采用Monte Carlo模擬方法計(jì)算出不同投資比例和置信水平的組合風(fēng)險(xiǎn)VaR和CVaR的值，并求出不同期望收益和置信水平下的最優(yōu)組合投資權(quán)重。實(shí)證結(jié)果表明，本文模型有利于投資者對投資權(quán)重的選擇。同時(shí)，由于金融資產(chǎn)不但存在方差風(fēng)險(xiǎn)，還存在時(shí)變偏度風(fēng)險(xiǎn)和時(shí)變峰度風(fēng)險(xiǎn)，這使得僅從金融資產(chǎn)的前兩階矩出發(fā)來研究風(fēng)險(xiǎn)變化顯得十分局限。GJRSK-M模型是描述金融資產(chǎn)的高階矩風(fēng)險(xiǎn)的有效工具，可對單個(gè)金融資產(chǎn)的分布進(jìn)行擬合，而M-Copula函數(shù)能連接組合金融資產(chǎn)的邊緣分布，因此本文又建立了M-Copula-GJRSK-M模型來研究滬深兩股票市場的相依性。實(shí)證表明，上證綜指和深圳成指對數(shù)收益率存在高階矩風(fēng)險(xiǎn)和風(fēng)險(xiǎn)的非對稱性，即指數(shù)下跌時(shí)，條件方差風(fēng)險(xiǎn)和條件高階矩風(fēng)險(xiǎn)會增大。 本文研究成果如下： ①提出了基于M-Copula-EGARCH-M-GED的投資組合模型。選用能刻畫風(fēng)險(xiǎn)溢價(jià)的EGARCH-M模型對各單個(gè)資產(chǎn)收益率進(jìn)行建模，選用M-Copula作為聯(lián)合分布連接函數(shù)，，用遺傳算法對模型中參數(shù)進(jìn)行計(jì)算，用基于GED分布的CVaR度量風(fēng)險(xiǎn)，利用Monte Carlo方法模擬求得不同投資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優(yōu)組合投資權(quán)重。 ②提出了基于M-Copula-GJRSK-M模型對滬深兩市的相依性進(jìn)行分析。選用GJRSK-M模型刻畫資產(chǎn)組合的邊緣分布，以反映單個(gè)資產(chǎn)價(jià)格波動的高階矩風(fēng)險(xiǎn)的時(shí)變性和非對稱性，再結(jié)合混合Copula函數(shù)建立M-Copula-GJRSK-M模型來研究組合資產(chǎn)的相依結(jié)構(gòu)并展開實(shí)證研究。 ③根據(jù)金融市場投資的聯(lián)動性和相關(guān)性，引入能夠囊括各種相關(guān)結(jié)構(gòu)變化的三種阿基米德Copula函數(shù),即選用了Gumble、Clayton和Frank Copula函數(shù)的線性組合來構(gòu)造混合Copula函數(shù)。由此更為靈活的描述具有復(fù)雜相關(guān)關(guān)系的事物之間的關(guān)聯(lián)度，如金融市場之間的相關(guān)關(guān)系。 ④采用一個(gè)服從2分布的M經(jīng)驗(yàn)統(tǒng)計(jì)量來評價(jià)M-Copula函數(shù)的擬合度，從而刻畫金融市場之間的相關(guān)模式；采用Ljung-Box Q檢驗(yàn)法和K-S檢驗(yàn)法對EGARCH-M模型的殘差序列的相關(guān)性和誤差分布的擬合度進(jìn)行檢驗(yàn)，進(jìn)而對EGARCH-M合理性進(jìn)行驗(yàn)證；運(yùn)用Gram-Charlier以及Leon對其定義式做了修正，利用正態(tài)分布展開對GJRSK-M模型進(jìn)行估計(jì)，從而能夠更精準(zhǔn)的捕捉到尾部分布和峰度的陡緩。 ⑤選取中國證券市場中具有代表性的上證綜指和深圳成指，利用統(tǒng)計(jì)和數(shù)據(jù)處理軟件，對本文提出模型、方法以及所得結(jié)論進(jìn)行實(shí)證分析，實(shí)證結(jié)論與理論推導(dǎo)結(jié)論吻合。
[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.
【學(xué)位授予單位】：重慶大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2014
【分類號】：F832.51;F224

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