金融自由化後，金融商品交易的多樣性在活絡金融市場方面佔有很重的份量，也使得投資者有更多樣化的投資管道及標地。投資者購買金融商品除了追求較高的報酬外，對於投資風險的管理也是不容乎視。2007年，美國的次級房貸subprimemortgage風爆使得雷曼兄弟和AIG集團爆發財務危機，正是投資者追求高報酬之後，在風險管理上並未妥善管理所造成。 　　 　　衡量風險時，通常會使用變異數或標準差當做衡量指標，即在衡量其波動性，因此波動性裏含有許多訊息。在本論文中，我們將探討波動性所透露出來的兩個訊息，一個是風險值(VaR)，文中將分別使用二種衡量可解釋長期記憶的GARCH模型探討台股指數期貨及新加坡的摩台股指數期貨這兩個期貨市場的VaR。另外則是試圖尋找出這兩個期貨市場殘差值的波動性之間的長期共整合關係。 本論文主要由三篇文章組成，第一篇是利用Baillie, Bollerslev, and Millelsen (1996) 所提出的長期記憶模型FIGARCH來計算台指期貨的風險值（VaR）；第二篇也是利用長期記憶模型來計算新加坡的摩台指期貨的風險值，但這次的長期記憶模型增加一個由Tse (1998)　提出的可以考慮不對稱性波動的FIAPARCH模型。 　　這兩個模型都搭配三種不同的分配來計算VaR，分別是Normal, Student-t和skewed Student-t分配；實證結果顯示，這兩個期貨市場報酬的波動皆具有長期記憶，表示之前影響指數期貨報酬率的因素對未來指數期貨報酬率會有較長時間的影響力。而在傳統認為差殘值服從常態分配的假定下所計算出的VaR的配適情況較以Student-t分配計算出的VaR的配適情況不具效率，這除了說明傳統的常態分配假說在計算此兩個指數期貨報酬率是不適用之外，亦得出他們是具有肥尾（厚尾）的現象。 　　第三篇則是結合前兩篇的結果來探討此兩個指數期貨報酬率之間的波動性是否具有長期關係。因為台指期貨報酬率與摩台指期貨報酬率的波動性皆具有長期記憶，故在此部分，利用Engle-Granger (1987) 的兩階段共整合模型來求此兩個指數期貨報酬率之間的波動性是否存在長期關係。實證結果顯示，他們確實存在長期共整合關係，且摩台指期貨報酬率的波動性較台指期貨報酬率的波動性強，因此我們可以在台指期貨市場買入期指，而在新加坡的摩台指期貨市場避險 / The finance commodity exchange's multiplicity holds the very heavy component in the detachable money market aspect, after the financial liberalization. It also enables the investor to have many chances and commodities of investment. The investor purchases the financial commodity besides the higher reward, and does not allow regarding investment risk's management to regard. In 2007, the securitization commodity violation of US's subprimemortgage explodes causes Lehman Brothers and the AIG group erupts the financial crisis. This is precisely the investor pursues the high reward, and their administration centers have not created properly in the risk management. When we measure risks, we usually adopt the variance or the standard deviation. That is to weight its property of volatilities. There is much information in the volatilities. In this thesis, we discussed two kinds of information which the property of volatilities discloses. One is the value at risk (VaR hereafter). In this article, we use long-term memory's GARCH model to explain that the VaR of Taiwan stock index futures returns and Singapore's MSCI Taiwan index futures returns. Moreover, we attempts to seek for whether there are long relationship of the residuals volatilities between these two futures markets. This thesis was combined by three essays. The first essay employed the FIGARCH model of Baillie, Bollerslev, and Millelsen (1996) to calculated the VaR of Taiwan stock index futures returns. The second essay employed the FIGARCH model and FIAPARCH model of Tse (1998) to calculated the VaR of Singapore's MSCI Taiwan index futures returns. We calculated the VaRs of the different two futures markets by using the FIGARCH and FIAPARCH models with three different distributions-normal, student-t and skewed student-t. The empirical results showed the two futures markets both has long memory. It is not efficient to calculated the VaRs by using the traditional normal distribution. The Student-t distribution fitted the model better than the normal distribution. The third essay, we employed the Engle-Granger (1987) two-step cointegration model to test whether there are long relationship of the residuals volatilities between the Taiwan stock index futures returns and Singapore's MSCI Taiwan index futures returns. The empirical results showed that there was fractional cointegration between the two futures markets and the volatility in Taiwan stock index futures market is about 83% of that in MSCI Taiwan Index Futures market.