Copula在不同市場指數上之關聯結構研究與風險管理應用

Research of Copula for Dependence Structure and Appiled Risk Management in Different Markets Index

翁瑜璟(Yu-Jing Weng)

指導教授 ： 王安岐

亞洲大學/管理學院/財務金融學系/碩士(2010年)

摘要

本研究利用Copula模型模擬台灣加權指數、上海綜合指數、日本日經225指數和南韓綜合指數兩兩之間的關聯結構，利用雷曼宣布倒閉日和MOU簽訂日作為分界點分為前後期。首先，估計出各國在不同時期指數報酬所服從的邊際分配，發現資料幾乎都具有厚尾的特性，使用Student-t分配為邊際較為適當，在MOU簽定後的上海綜合指數和日本日經225指數對數報酬則是服從常態分配。其次，建構四種常用的Copula模型，並估計其相關參數，選出較適之Copula。最後，利用適當之Copula做風險值的估計，雖然使用Student-t分配與常態分配都有高低估的現象，但是使用Student-t分配分別估計各國指數對數報酬的風險值比用常態分配的誤差來的小，所以較為適合且有用的。同時也利用適當Copula模型結構來衡量兩個市場報酬投資組合所面臨之風險機率，估計之結果顯示與實際情況是相符的。

關鍵字

Copula ； 關聯結構 ； 風險值

並列摘要

This research takes Copula model to simulate dependence structures between two indexes and two indexes including Taiwan weighted index, Shanghai Composite Index, Japan's Nikkei 225 index and South Korea's composite index, and uses Lehman’s announcement of bankruptcy and the date of contract of MOU as boundary to show before and after periods. First, this study estimates the index return margin distribution of the country at different periods. The margin distribution almost has the characteristics of the heavy tail, using Student-t distribution is more appropriate for the margin, but Shanghai and Japan is normal distribution after the MOU had been signed. Second, this study constructs four types of common using Copula model, estimates the parameter of correlation, and selects the appropriate Copula. Last, this research uses the suitable Copula to estimate value-at-risk(VaR), using Student-t distribution and normal distribution have phenomena of overestimate and underestimate, but the errors of Student-t distribution is smaller than those of normal distribution; it is more appropriate and useful. Meanwhile, using the appropriate Copula model measures the risky probability with two markets portfolio of return, the result of this research is coincided with real market circumstances.

並列關鍵字

Copula ； Dependence Structure ； VaR

參考文獻

4.曾毅豪，2007，關聯結構在金融市場風險管理之研究，「國立成功大學統計學研究所碩士論文」。

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