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.
