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博碩士論文 etd-0702107-162427 詳細資訊
Title page for etd-0702107-162427
論文名稱
Title
利用Conditional-Copula-GARCH方法估計風險值
Estimate Value at Risk of Portfolio by Conditional-Copula-GARCH Method
系所名稱
Department
畢業學年期
Year, semester
語文別
Language
學位類別
Degree
頁數
Number of pages
59
研究生
Author
指導教授
Advisor
召集委員
Convenor
口試委員
Advisory Committee
口試日期
Date of Exam
2007-06-21
繳交日期
Date of Submission
2007-07-02
關鍵字
Keywords
風險值
VC, Kendall, MLE, Copula, IFM, EWMA
統計
Statistics
本論文已被瀏覽 5722 次,被下載 15
The thesis/dissertation has been browsed 5722 times, has been downloaded 15 times.
中文摘要
Copula是用來描述多元隨機變數間相關性結構的一個統計方法,且近年已經顯著成為財務上用來控管風險因子的新工具,例如廣泛運用於金融機構風險管理中的風險值。在本篇論文中,Copula跟GARCH模型妥善地做了一個結合,新的方法Conditional-Copula-GARCH可以用來衡量財務資料的相關性,跟計算投資組合的風險值。Copula-GARCH模型藉由把邊際分配跟相關性分開,提供了一個非常彈性的聯合分布,不同於傳統用來估計風險值的方法,例如變異數共變異數法或蒙地卡羅法皆要求聯合分佈已知。這篇文章利用Copula-GARCH方法來估計投資組合的風險值,投資組合包括NASDAQ跟台灣加權股價指數(TAIEX)。
Abstract
Copula functions represent a methodology which can describe the dependence structure of multi-dimension random variable, and has recently become the most significant new tool to handle risk factors in finance such as Value-at Risk( VaR) which was probably the most widely used risk measure in financial institutions. In this paper, Copula and the forecast function of Garch model are well combined, and a new method Conditional-Copula-Garch is built for measure the dependence of financial data and compute the VaR of portfolios. Copula-Garch models allow for very flexible joint distribution by splitting the marginal behaviors form the dependence relation unlike the traditional approaches for the estimation VaR, such as variance-covariance, and the Monte Carlo approaches whereas demand the joint distribution to be known. This work presents an application of the Copula-Garch model in the estimation of VaR of a portfolio composed by NASDAQ and TAIEX (Taiwan stock exchanged capitalization weighted index) stock indices.
目次 Table of Contents
Contents
1、Introduction……………………………………………………………………….1
2、Literature Review………………………………………………………………... .3
3、Model for the marginal distribution…………………………………………….. 4
3.1、GARCH-N and GARCH-T model ………………………………………..5
3.2、GJR-N and GJR-T model ………………………………………..………7
4、Copula Theory …………………………………………………………………….8
4.1、Definition …………………………………………………………………..8
4.2、Sklar’s theorem ……………………………………………………………9
4.3、 The Frechet-Hoeffding Bounds …………………………………….…..10
4.4、 Some families of copula …………………………………..…………..…10
4.4.1、Gaussian copula ……………………………………………….…..11
4.4.2、Student t copula ……………………………………………….…..11
4.4.3、Archimedean copulae ……………………………………….…….12
4.4.3.1、Clayton copula and Rotated-Clayton copula ………….....13
4.4.3.2、Plackett copula ……………………………………………..13
4.4.3.3、Frank copula ……………………………………………….14
4.4.3.4、Gumbel copula and Rotated-Gumbel copula ……………14
4.5、 Measures of Dependence ……………………………………………….15
4.5.1、Linear correlation coefficient …………………………………….15
4.5.2、Rank correlation coefficients ……………………………….…….15
4.5.2.1、Spearman’s rho ……………………………………………16
4.5.2.2、Kendall’s tau ……………………………………………….16
4.5.3、Tail Dependence Coefficients …………………………………….18
5、Estimation Procedures …………………………………………………….…….20
5.1、Maximum Likelihood Method …………………………………….…….20
5.2、IFM METHOD …………………………………………………………...21
5.3、Conditional situation ……………………………………………………..22
5.4、Selection of the copula function …………………………………………23
5.4.1、Akaike information criterion (AIC) …………………………….23
5.4.2、Bayesian information criterion (BIC) …………………………...23
6.、Empirical results ………………………………………………………………..24
6.1、The data …………………………………………………………………...24
6.2 、The marginal distribution ……………………………………………...26
6.3、Copula modeling ………………………………………………………….30
6.4、Estimate the value at risk (VaR) .……………………………………….34
6.5、Comparison with traditional VaR estimation ………………………….37
7、Conclusion ……………………………………………………………………….41
Reference ……………………………………………………………………………42
Appendix ……………………………………………………………………………45
參考文獻 References
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