本文選題：混合Copula + GARCH模型　； 參考：《中央民族大學(xué)》2013年碩士論文

【摘要】：在過(guò)去的一段時(shí)間內(nèi),金融市場(chǎng)的相關(guān)關(guān)系被大量研究。由于Copula模型不僅考慮了金融時(shí)間序列間的相關(guān)程度,也將相關(guān)結(jié)構(gòu)考慮其中,已經(jīng)成為研究金融風(fēng)險(xiǎn)領(lǐng)域的重要工具。 在實(shí)際應(yīng)用中,想用一個(gè)單一的Copula函數(shù)全面刻畫(huà)金融市場(chǎng)中的相關(guān)關(guān)系是很難的,所以需要構(gòu)建一個(gè)更為靈活的Copula函數(shù),以便可以更好的描述復(fù)雜的金融市場(chǎng)之間的相關(guān)關(guān)系。通過(guò)考慮不同Copula函數(shù)的特性,選取不同特征的Copula函數(shù)以不同的權(quán)重組合在一起,形成一個(gè)新的Copula函數(shù)——即混合Copula函數(shù)(M-Copula)。相對(duì)于某一特定的Copula函數(shù)來(lái)說(shuō),構(gòu)建混合Copula函數(shù)的優(yōu)勢(shì)是混合Copula可以包含不同類(lèi)型的Copula函數(shù),即為混合Copula函數(shù)通過(guò)相關(guān)參數(shù)來(lái)度量變量之間的相關(guān)程度,而線性組合系數(shù)可以捕獲相依結(jié)構(gòu)之間的不同模式。而且,從經(jīng)驗(yàn)來(lái)看,混合Copula函數(shù)可以通過(guò)自由選擇不同的Copula函數(shù)來(lái)建立相關(guān)結(jié)構(gòu),與單一的Copula函數(shù)相比,能更好的描述真實(shí)相關(guān)結(jié)構(gòu)。 由于金融市場(chǎng)中的資產(chǎn)回報(bào)分布有明顯的尖峰厚尾特性,所以假設(shè)正態(tài)分布會(huì)低估尾部的極端風(fēng)險(xiǎn)。極值理論可以針對(duì)數(shù)據(jù)的尾部建立模型,這種方法不需要假設(shè)金融資產(chǎn)收益的分布,而是運(yùn)用數(shù)據(jù)直接擬合尾部的分布,通過(guò)這種方法可以很好地捕捉極端事件發(fā)生的概率,極值理論在度量高置信度風(fēng)險(xiǎn)方面能夠顯示出獨(dú)特的優(yōu)勢(shì)。 我們選取2002年1月4日至2012年12月31日上證工業(yè)指數(shù)、商業(yè)指數(shù)和公用指數(shù)三個(gè)行業(yè)指數(shù)序列的2666組數(shù)據(jù)進(jìn)行實(shí)證分析。對(duì)于每一個(gè)指數(shù)序列分別擬合GARCH類(lèi)模型來(lái)描述邊緣分布,運(yùn)用極值理論對(duì)數(shù)據(jù)尾部進(jìn)行改進(jìn),選取阿基米德Copula函數(shù)中的Gumbel Copula、Clayton Copula和Frank Copula來(lái)構(gòu)造M-Copula模型。從中可以看到：(1)利用極值理論中的POT模型改進(jìn)了邊緣分布,使得風(fēng)險(xiǎn)評(píng)估更加貼近真實(shí)。(2)結(jié)合混合Copula模型以及蒙特卡洛模擬來(lái)計(jì)算VAR是有效的,而某一個(gè)單一的Copula函數(shù)會(huì)低估了真實(shí)存在的風(fēng)險(xiǎn)值。這說(shuō)明混合Copula函數(shù)能夠更加真實(shí)的反應(yīng)潛在的相關(guān)結(jié)構(gòu)。
[Abstract]:Over the past period of time, the relationship between financial markets has been a lot of research. Because the Copula model not only considers the degree of correlation among financial time series, but also takes the correlation structure into account, it has become an important tool in the field of financial risk research. In practical application, it is difficult to describe the correlation relationship in financial market with a single Copula function, so it is necessary to construct a more flexible Copula function to describe the correlation relationship between complex financial markets better. By considering the characteristics of different Copula functions, Copula functions with different characteristics are selected and combined with different weights to form a new Copula function, that is, mixed Copula function (M-Copula). The advantage of building a hybrid Copula function over a particular Copula function is that the hybrid Copula can contain different types of Copula functions, that is, the hybrid Copula function measures the correlation between variables by correlation parameters. Linear combination coefficients can capture different patterns between dependent structures. Moreover, from the experience, the mixed Copula function can establish the correlation structure by choosing different Copula functions freely. Compared with the single Copula function, the hybrid Copula function can describe the real correlation structure better. Because the distribution of return on assets in financial markets has the characteristic of peak and thick tail, it is assumed that the normal distribution will underestimate the extreme risk of tail. The extreme value theory can build a model for the tail of the data. This method does not need to assume the distribution of the return on the financial assets, but uses the data to fit the distribution of the tail directly. By this method, the probability of extreme events can be captured very well. Extreme value theory can show unique advantages in measuring the risk of high confidence. From January 4, 2002 to December 31, 2012, we choose 2666 sets of data from Shanghai Stock Exchange Industrial Index, Business Index and Public Index to carry out empirical analysis. For each exponential sequence, the GARCH class model is fitted to describe the edge distribution, and the extreme value theory is used to improve the tail of the data. The Gumbel Copula Clayton Copula and Frank Copula in the Archimedes Copula function are selected to construct the M-Copula model. We can see that: 1) using the POT model in extreme value theory to improve the edge distribution, make the risk assessment more close to the reality.) it is effective to combine the mixed Copula model and Monte Carlo simulation to calculate the VAR. A single Copula function underestimates the real risk. This shows that the mixed Copula function can reflect the potential correlation structure more realistically.
【學(xué)位授予單位】：中央民族大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2013
【分類(lèi)號(hào)】：F224;F830.91;O211.4

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本文編號(hào)：1800797