【摘要】：隨著金融全球化,各國(guó)金融市場(chǎng)之間的關(guān)聯(lián)性越來(lái)越密切,那么準(zhǔn)確地度量金融市場(chǎng)間的相關(guān)性越來(lái)越重要。由于傳統(tǒng)的相關(guān)性分析方法只能度量變量間的線性相關(guān)關(guān)系,且目前的金融市場(chǎng)間的相關(guān)性已經(jīng)呈現(xiàn)出非線性、非對(duì)稱(chēng)和厚尾相依性等特點(diǎn),所以原來(lái)的方法已遠(yuǎn)遠(yuǎn)不能夠滿足要求。Copula方法的出現(xiàn)給度量多變量間非線性相關(guān)關(guān)系提供了一個(gè)有效的工具。 本文主要研究多元Copula函數(shù)在金融風(fēng)險(xiǎn)管理上的一些應(yīng)用,首先介紹了傳統(tǒng)的多元Copula函數(shù)的類(lèi)型及性質(zhì),并結(jié)合GARCH模型構(gòu)建了Copula-GARCH模型來(lái)刻畫(huà)金融時(shí)間序列間的相依結(jié)構(gòu)。然后在傳統(tǒng)多元Copula-GARCH模型的基礎(chǔ)上,引入了最新的多元藤結(jié)構(gòu)Pair-Copula來(lái)構(gòu)建高維相關(guān)關(guān)系,由于它在刻畫(huà)高維資產(chǎn)組合中兩兩資產(chǎn)間尾部相關(guān)性時(shí)可以根據(jù)實(shí)際數(shù)據(jù)的特征來(lái)選擇不同類(lèi)型的Copula函數(shù),從而能夠更好的刻畫(huà)金融資產(chǎn)間尾部的相關(guān)性。 另外在Pair-Copula函數(shù)模型的選擇上面,選擇了三種類(lèi)型的Copula函數(shù)：t-Copula、Clayton Copula和SJC Copula,二元t-Copula可以很好地反映變量間的上下尾相關(guān)性,Clayton Copula則可以快速捕捉下尾無(wú)條件相關(guān)的變化,SJC Copula可以快速捕捉下尾條件相關(guān)的變化。采用這三種函數(shù)類(lèi)型,既關(guān)注了尾部的整體相關(guān)又特別描述了下尾的相關(guān)。 在實(shí)證部分,以我國(guó)外匯市場(chǎng)間的美元、日元、歐元、英鎊對(duì)人民幣四種匯率收益率序列為研究對(duì)象,分別采用多元正態(tài)Copula、 t-Copula函數(shù)與Pair-Copula函數(shù)來(lái)描述變量間的相依結(jié)構(gòu),并通過(guò)擬合優(yōu)度檢驗(yàn)得知,Pair-Copula在描述變量間的相依結(jié)構(gòu)時(shí)更加準(zhǔn)確。再將Pair-Copula-GARCH模型與Monte Carlo仿真技術(shù)相結(jié)合,計(jì)算了此模型下的多資產(chǎn)組合的VaR及ES,并與傳統(tǒng)多元Copula-GARCH模型下計(jì)算出的資產(chǎn)組合VaR進(jìn)行了比較,并給出了在風(fēng)險(xiǎn)最小原則下投資組合的最優(yōu)解。結(jié)果表明,在所選擇的樣本期間內(nèi),基于Pair-Copula模型的預(yù)測(cè)的VaR結(jié)果要好于多元正態(tài)或多元t-Copula模型的預(yù)測(cè)效果,由此可以驗(yàn)證Pair-Copula-GARCH模型在構(gòu)建多元相關(guān)結(jié)構(gòu)的優(yōu)越性。
[Abstract]:With the development of financial globalization, it is more and more important to measure the correlation between financial markets accurately. Because the traditional correlation analysis method can only measure the linear correlation between variables, and the correlation between financial markets has become nonlinear, asymmetric and thick tail. The Copula method provides an effective tool to measure the nonlinear correlation among multivariates.
This paper mainly studies the application of multivariate Copula function in financial risk management. Firstly, the types and properties of traditional multivariate Copula function are introduced, and then a Copula-GARCH model is constructed to describe the dependence structure of financial time series. Then, based on the traditional multivariate Copula-GARCH model, the newest one is introduced. Pair-Copula, a multivariate rattan structure, is used to construct the high-dimensional correlation. Because it can select different types of Copula functions according to the characteristics of the actual data when describing the tail correlation between two assets in a high-dimensional portfolio, it can better describe the tail correlation between financial assets.
In addition, on the selection of Pair-Copula function model, three types of Copula functions are selected: t-Copula, Clayton Copula and SJC Copula, binary t-Copula can well reflect the upper and lower tail correlation between variables, Clayton Copula can quickly capture the lower tail unconditionally related changes, SJC Copula can quickly capture the lower tail conditional phase. With these three types of functions, both the overall tail correlation and the tail correlation are described in particular.
In the empirical part, we take the US dollar, Japanese yen, Euro and Pound-to-Renminbi exchange rate return series as the research object, and use the multivariate normal Copula, t-Copula function and Pair-Copula function to describe the dependence structure between variables. Through the goodness of fit test, we find that Pair-Copula describes the dependence between variables. Combining Pair-Copula-GARCH model with Monte Carlo simulation technique, VaR and ES of multi-asset portfolio are calculated, and compared with VaR of portfolio calculated by traditional multi-element Copula-GARCH model, and the optimal solution of portfolio under the principle of minimum risk is given. During the selected sample period, the predicted VaR results based on Pair-Copula model are better than those based on multivariate normal or multivariate t-Copula model, which verifies the superiority of Pair-Copula-GARCH model in constructing multivariate correlation structure.
【學(xué)位授予單位】：浙江工商大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2012
【分類(lèi)號(hào)】：F830.59;F224;F830.7

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