期貨契約向來被視為規避現貨價格變動風險之良好工具，許多學者也陸續提出不同方法來評估現貨和期貨間的關聯性，希望能藉此來提升避險績效。近年來在財務領域上越來越多學者使用Sklar (1959) 所提出的Copula函數來評估變數間的關聯性，許多相關文獻指出根據Sklar定理可將聯合機率分配拆解成期貨和現貨的邊際分配及Copula函數兩個部分，使得在設定現貨和期貨報酬率的聯合分配上更有彈性。
   因此，本文將針對Copula函數和邊際分配間的關係進行推論與說明，來探討是否可以任意選取Copula函數和邊際分配來配適變數間的聯合機率分配。而實證方面，本文使用過去常見的避險模型，OLS模型、GARCH-N模型和GARCH-t模型，對台灣股價指數現貨和期貨來實行樣本外避險。推論結果顯示，當邊際分配決定後即確定Copula函數的型態，而選定某Copula函數即隱含其邊際分配已被確定，所以不可任意選取Copula函數和邊際分配來配適聯合機率分配。實證結果顯示，兩種雙變量GARCH模型避險績效差不多，且都優於OLS模型的避險績效結果。

Futures contracts are seen to be a good tool to avoid the risk of changes in spot prices. Many hope to improve the hedging performance by proposing different methods to assess the interdependence between spot prices and futures contracts. In recent years, many literary works use the Copula function to capture the dependence between the two. Many related academic papers point out that joint distribution can be split into two parts: marginal distributions and the Copula function by Sklar theory. As such, the proposed models can specify the joint distribution of the spot price and futures contract returns with greater flexibility.
  Therefore, in order so we can choose between any Copula function and specify the joint distribution with marginal distributions, we infer and explain the relationship between them in this article. We also use three models to estimate the optimal hedge ratio including: OLS, GARCH-N and GARCH-t. The results show that we cannot specify the joint distribution by arbitrarily choosing the Copula function and marginal distributions. The empirical results show that in the out-of-example test, the hedging performance of the two GARCH models there is no difference and their performance altogether better than the OLS model.

目 錄
表 目 錄	V
圖 目 錄	VI
第一章 緒論	1
第一節	研究背景與動機	1
第二節	研究目的	2
第三節	研究流程	4
第四節	研究架構	5
第二章 理論基礎與文獻回顧	6
第一節	股價指數期貨簡介	6
第二節	避險理論回顧	10
第三節	避險模型	14
第四節	避險實證相關文獻	20
第五節	Copula實證相關文獻	23
第三章 研究方法	26
第一節	單根檢定	26
第二節	ARCH效果檢定	28
第三節	避險比率的估計	30
第四節	GARCH 模型介紹	31
第五節	關聯函數(Copula)之介紹	38
第六節	實證模型	41
第七節	避險績效衡量	44
第四章 實證結果與分析	46
第一節	資料來源與處理	46
第二節	單根檢定	49
第三節	ARCH效果檢定	49
第四節	不同避險模型下之樣本外避險績效比較	50
第五節	Copula函數與邊際分配間的關係之推論與說明	54
第五章 結論	58
參考文獻	60
中文部分	60
英文部分	61

 
表 目 錄
【表2-1】以台灣股價指數為標的之股價期貨契約	9
【表4-1】台灣股價指數現貨與期貨日報酬率之基本統計量	47
【表4-2】台灣股價指數單根檢定結果	49
【表4-3】台指現貨與期貨ARCH效果檢定結果	50
【表4-4】雙變量GARCH模型參數估計結果	52
【表4-5】樣本外不同避險模型之平均避險比率	53
【表4-6】樣本外不同避險模型避險效果之比較	54

 
圖 目 錄
【圖1-1】研究流程圖 	4
【圖4-1】台灣股價指數現貨與期貨價格走勢圖 	48
【圖4-2】台灣股價指數現貨與期貨報酬率走勢圖	48
【圖4-3】樣本外之移動視窗方法 	51

中文部分
1.	余尚武與賴昌作，(2000)，「股價指數期貨之避險比率與避險效益」，管理研究學報，第1卷第1期，頁1~31。
2.	李享泰與柯冠成，(2010)，「台灣股價指數期貨的交叉避險績效」，期貨與選擇權學刊，第3卷第1期，頁33~55。
3.	邱建良、魏志良、吳佩珊與邱哲修，(2004)，「TAIFEX與MSCI台股指數期貨與現貨直接避險策略之研究」，商管科技季刊，第5卷第2期，頁169~184。
4.	黃景明，(2002)，台灣股價指數期貨最適避險策略之研究，淡江大學財務金融學系碩士論文。
5.	葉怡君，(2005)，以Copulas測度市場風險之探討，交通大學產業經濟學系碩士論文。
6.	廖四郎、李福慶，(2005)，「擔保債權憑證之評價-Copula分析法」，台灣金融財務季刊，第六輯第二期，頁53~84。
 
英文部分
1.	Anderson, R. W., and Danthine, J. P., (1981), “Cross hedging,” Journal of Political Economy, Vol. 89, pp. 1182-1196.
2.	Benet, B. A., (1992), “Hedge period length and ex-ante futures hedging effectiveness: The case of foreign-exchange risk cross hedges.” Journal of Futures Markets, Vol. 43, No. 1, pp. 163-175.
3.	Bollerslev, T., (1986), “Generalized autoregressive conditional heteroscedasticity,” Journal of Econometrics, Vol. 31, pp. 307-327.
4.	Bollerslev, T., Engle, R. F., and Wooldridge, J. M., (1988), “A capital asset pricing model with time-varying covariances,” Journal of Political Economy, Vol. 96, pp. 116-131.
5.	Bollerslev, T., (1990), “Modeling the coherence in short-run nominal exchange rates: A multivariate generalized ARCH approach,” Review of Economics and Statistics, Vol. 72, pp. 498-505.
6.	Choudhry, T., (2003), “Short-run deviations and optimal hedge ratio：Evidence from Stock,” Journal of Multinational Financial Management, Vol. 13, pp.171-192.
7.	Chiu et al., (2005), “Hedging with floor-traded and e-mini stock index futures.” Quarterly Journal of Business and Economics, Vol. 44 (3/4), pp. 49-68.
8.	Dickey, D., and Fuller, W., (1979), “Distribution of estimators for autoregressive time series with a unit root,” Journal of the American Statistical Association, Vol. 74, pp.427-431.
9.	Dickey, D. A., and Fuller, W. A., (1981), “Likelihood ratio statistics for autoregressive time series with a unit root,” Econometrica, Vol. 49 (4), pp. 1057-1072.
10.	Ederington, L. H., (1979), “The hedging performance of the new future markets,” Journal of Finance, Vol. 34, pp. 157-170.
11.	Engle, R. F., (1982), “Autoregressive conditional heteroscedasticity with estimates of the variance of U.K. inflation,” Econometrica , Vol. 50, pp. 987-1008.
12.	Engle, R. F., and Granger, C. W. J., (1987), “Co-integration and error correction：representation, estimation and testing,” Econometrica, Vol. 55, pp. 251-276.
13.	Engle, R. F., and Kroner, K. F., (1995), “Multivariate simultaneous generalized ARCH,” Econometric Theory, Vol. 11, pp.122-150.
14.	Engle, R. F., (2002), “Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models,” Journal of Business and Economic Statistics, Vol. 20 (3), pp. 339-350.
15.	Hsu, C. C., Tseng, C. P., and Wang, Y. H., (2008), “Dynamic hedging with Futures: a Copula-based GARCH model,” Journal of Futures Markets, Vol. 28, No. 11, pp.1095-1116.
16.	Johnson, L. L., (1960), “The theory of hedging and speculation in commodity futures,” Reviews of Economic Studies, Vol. 27, No 3, pp. 139-151.
17.	Kroner, K. F., and Sultan, J., (1991), “Exchange rate volatility and time varying hedge ratios,” Pacific-Basin Capital Markets Research, Vol. 2, pp. 397-412.
18.	Lai, Y., Chen, C. W. S., and Gerlach, R., (2009), “Optimal dynamic hedging via Copula threshold GARCH models,” Mathematics and Computers in Simulation, Vol. 79, pp.2609-2624.
19.	Markowitz, H., (1952), “Portfolio selection,” Journal of Finance, Vol. 7,No. 1, pp. 77-91.
20.	Park, T. H., and Switzer, L. N., (1995), “Bivariate GARCH estimation of the optimal hedge ratios for stock index future: A note,” Journal of Futures Markets, Vol. 15, pp. 61-67.
21.	Sklar, A., (1959), “Fonctions de repartition a n dimensions et leurs marges,” Publ.  Int. Statistique Univ. Paris, Vol. 8, pp. 229-231.
22.	Sims, C. A., (1980), “Macroeconomics and reality,” Econometrica, Vol. 48, pp. 1-48.
23.	Stein, J. L., (1961), “The simultaneous determination of spot and futures prices,” American Economic Review, Vol. 51, pp. 1012-1025.
24.	Witt, S. F. and Martin, C. A., (1987), “Econometric models for forecasting international tourism demand,” Journal of Travel Research, Vol. 25 (3), pp. 23-30.
25.	Working, H., (1953), “Futures trading and hedging,” American Economic Review, Vol. 43, No. 3, pp. 314-343.