本文選題：Copula　切入點(diǎn)：函數(shù)　出處：《長(zhǎng)春工業(yè)大學(xué)》2012年碩士論文

【摘要】：金融市場(chǎng)間的相依關(guān)系越來(lái)越密切,準(zhǔn)確地刻畫高頻率變化的金融市場(chǎng)之間的相依結(jié)構(gòu)是金融研究領(lǐng)域重要的課題,這對(duì)于金融市場(chǎng)運(yùn)行機(jī)制的建立和金融決策都具有非常重要的理論和現(xiàn)實(shí)意義。隨著金融的全球一體化,金融市場(chǎng)的風(fēng)險(xiǎn)管理越來(lái)越被投資者和管理者所重視。 關(guān)于金融市場(chǎng)相依性方面,國(guó)內(nèi)目前的研究大多局限在分析滬深兩市之間的日周期的相關(guān)性。對(duì)于我國(guó)股指期貨市場(chǎng)和股票市場(chǎng)的相依性方面的研究較少。因此,本文從高頻數(shù)據(jù)極值這樣一個(gè)全新的視角來(lái)研究金融市場(chǎng)的相依性和風(fēng)險(xiǎn)控制。由于金融市場(chǎng)的收益率大多數(shù)呈現(xiàn)尖峰厚尾分布,所以不能用傳統(tǒng)的正態(tài)分布或t分布來(lái)描述變量間的關(guān)系。Copula函數(shù)是研究隨機(jī)變量間相依性的一個(gè)新的統(tǒng)計(jì)工具,它連接了隨機(jī)變量的聯(lián)合分布和邊緣分布,不同族Copula函數(shù)有不同的研究應(yīng)用范圍。本文介紹了Copula函數(shù)基本理論及Copula函數(shù)的參數(shù)估計(jì)和檢驗(yàn)方法。在金融市場(chǎng)的風(fēng)險(xiǎn)控制中介紹了VaR理論的研究方法,VaR的計(jì)算方法等。 本文以我國(guó)股指期貨指數(shù)和上證指數(shù)2011年10月24到2011年11月18日的5分鐘極值序列為研究對(duì)象,對(duì)股指期貨IF1112指數(shù)和上證000001指數(shù)5分鐘極大值和極小值的收益序列的相依性進(jìn)行了研究。對(duì)對(duì)數(shù)收益率序列進(jìn)行正態(tài)性檢驗(yàn),結(jié)果都拒絕正態(tài)假設(shè)。接著用Gumbel、Clayton、Frank和GS Copula函數(shù)對(duì)數(shù)據(jù)進(jìn)行擬合,通過(guò)用Q-Q圖、K-S檢驗(yàn)發(fā)現(xiàn),用Gumbel函數(shù)描述股指期貨IF1112指數(shù)和上證000001指數(shù)5分鐘極大值和極小值的收益序列相依性最為合適,并對(duì)股指期貨IF1112指數(shù)和上證000001指數(shù)5分鐘極大值和極小值的收益序列的尾部相關(guān)性進(jìn)行研究,發(fā)現(xiàn)上股指期貨IF1112指數(shù)和上證000001指數(shù)5分鐘極大值和極小值的收益序列之間呈現(xiàn)明顯的上尾相關(guān)�；诓煌椒ǚ治隽斯芍钙谪浿笖�(shù)極大值收益率序列的VaR,得到了VaR序列,給投資者或管理者從定量的角度提供了對(duì)風(fēng)險(xiǎn)控制的參考。
[Abstract]:The dependence of financial markets is becoming more and more close. It is an important subject in the field of financial research to accurately depict the dependence structure of financial markets with high frequency changes.This is of great theoretical and practical significance to the establishment of financial market operation mechanism and financial decision-making.With the global integration of finance, the risk management of financial market is paid more and more attention by investors and managers.Regarding the dependence of financial markets, most of the current studies are confined to the analysis of the correlation of the daily cycle between Shanghai and Shenzhen stock markets.There are few researches on the dependence of stock index futures market and stock market in China.Therefore, this paper studies the dependence and risk control of financial markets from the perspective of high frequency data extremum.Because most of the returns of financial markets show peak and thick tail distribution, the traditional normal distribution or t distribution can not be used to describe the relationship between variables. Copula function is a new statistical tool to study the dependence of random variables.It connects the joint distribution and edge distribution of random variables. Different families of Copula functions have different applications.In this paper, the basic theory of Copula function and the parameter estimation and test method of Copula function are introduced.In the risk control of financial market, this paper introduces the research method of VaR theory and the calculation method of VaR.In this paper, we study the 5-minute extreme value series of China's stock index futures index and Shanghai stock index from October 24, 2011 to November 18, 2011.This paper studies the dependence of the return sequence of the IF1112 index and the 000001 index of Shanghai stock index futures.The normal test of logarithmic return series is carried out, and the results reject the normal hypothesis.Then the data are fitted by Gumbelton Clayton Frank and GS Copula function. By using Q-Q chart K-S test, it is found that the Gumbel function is the most suitable to describe the dependence of the 5-minute maximum and minimum return sequence of IF1112 index and 000001 index in Shanghai stock index futures.The tail correlation of the five minute maximum and minimum value of IF1112 index and 000001 index of stock index futures is studied.It is found that the IF1112 index and the 000001 index of Shanghai stock index show a significant correlation between the return sequence of the maximum value and the minimum value in 5 minutes.Based on different methods, this paper analyzes the VaR of the maximum return rate of stock index futures index, and obtains the VaR sequence, which provides a reference to risk control for investors or managers from a quantitative point of view.
【學(xué)位授予單位】：長(zhǎng)春工業(yè)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2012
【分類號(hào)】：F224;F832.5

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