本文選題：股票市場 + Copula函數(shù)�。� 參考：《湖南大學(xué)》2014年碩士論文

【摘要】：現(xiàn)如今，股票市場不管是一級市場還是二級市場，都是監(jiān)管者與投資者關(guān)注的核心，也是投資者與籌資者互相博弈的一個市場，而市場分析者在投資者與籌資者之間起到橋梁作用。市場分析者在研究金融市場上獨特的尖峰與厚尾特性的過程中，，使得以往使用基于正態(tài)分布假設(shè)的分析突顯不足，本文主要利用Clayton、Gumbel及Frank三個Copula函數(shù)構(gòu)建的混合Copula函數(shù)將金融市場之間的結(jié)構(gòu)進行整體刻畫。 本文前幾章對Copula函數(shù)的含義與性質(zhì)進行了簡單回顧，闡述了幾種通用的Copula函數(shù)，并將該函數(shù)的參數(shù)與幾種相關(guān)系數(shù)之間的對應(yīng)關(guān)系進行了描述。接著介紹了金融市場上時間序列模型，包括參數(shù)與非參數(shù)估計，主要介紹核估計法。然后講述了貝葉斯理論及貝葉斯的計算方法，并且將基于Mix-Copula函數(shù)與經(jīng)驗Copula的三元線性模型的似然函數(shù)與后驗密度函數(shù)進行了貝葉斯推斷。將bayesian理論運用到Mix-Copula函數(shù)當(dāng)中權(quán)重系數(shù)的估計，對Experience-Copula函數(shù)與Mix-Copula函數(shù)進行線性擬合。 文中將上證指數(shù)與深圳成指2009~2013年每日的歷史收盤價作為樣本進行分析，分析數(shù)據(jù)的基本統(tǒng)計特征，利用核估計法對兩個樣本變量進行邊緣分布估計，然后利用阿基米德Copula函數(shù)建立四種不同Copula函數(shù)進行分析，運用歐氏距離對四種不同的函數(shù)進行擬合檢驗，最后選出一組相對最優(yōu)的Copula函數(shù)，并將利用貝葉斯方法與非線性規(guī)劃方法估計出的結(jié)果進行比較，通過比較結(jié)果來看，貝葉斯方法也能達到經(jīng)典方法的效果，甚至更好，基于貝葉斯的混合Copula函數(shù)同時得到兩者之間的上尾相關(guān)系數(shù)與下尾相關(guān)系數(shù)。
[Abstract]:Nowadays, the stock market, whether it is a primary market or a secondary market, is the core of the attention of regulators and investors, and is also a market in which investors and financiers play games against each other. Market analysts act as a bridge between investors and financiers. Market analysts in the process of studying the unique peak and thick tail characteristics of financial markets make the past analysis based on the normal distribution hypothesis highlighted the insufficiency. In this paper, the structure of financial markets is described as a whole by using the mixed Copula functions constructed by Clayton Gumbel and Frank functions. In the first chapters of this paper, the meaning and properties of Copula function are briefly reviewed, several general Copula functions are expounded, and the corresponding relations between the parameters of the function and several correlation coefficients are described. Then it introduces the time series model in financial market, including parametric and nonparametric estimation, and mainly introduces kernel estimation method. Then, the Bayesian theory and the calculation method of Bayesian are described, and the Bayesian inference of the likelihood function and the posterior density function of the ternary linear model based on Mix-Copula function and empirical Copula is carried out. The bayesian theory is applied to the estimation of the weight coefficient in the Mix-Copula function, and the linear fitting between the Experience-Copula function and the Mix-Copula function is carried out. In this paper, the daily historical closing price of Shanghai Stock Exchange Index and Shenzhen Chengdu Index from 2009 to 2013 are analyzed as samples, the basic statistical characteristics of the data are analyzed, and the marginal distribution of two sample variables is estimated by using kernel estimation method. Then four different Copula functions are established by using Archimedes Copula function to analyze, and Euclidean distance is used to test the fitting of four different functions. Finally, a group of relatively optimal Copula functions are selected. The results estimated by using Bayesian method and nonlinear programming method are compared. The results show that the Bayesian method can also achieve the effect of classical method, or even better. The mixed Copula function based on Bayesian is used to obtain the upper tail correlation coefficient and lower tail correlation coefficient.
【學(xué)位授予單位】：湖南大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2014
【分類號】：F224;F830.9

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