本文應用極值理論估算國內現有臺股、金融與電子等三種指數期貨之理論結算保證金水準，並以高斯-牛頓法(Gauss-Newton method)求算非線性迴歸模型中之各種參數。由於樣本數不足將會降低極值分配的近似效果與模型中各種參數估計的精確度，因此，為了克服樣本可能過少的問題，本文以日內5分鐘的價格資料來估計保證金水準。實證結果針對6種不同之極值取樣的交易時段時(n)，分別求出上述三種指數期貨所適合的n值。此外，實證結果亦發，在相同之違約機率下，電子期貨的波動性最為劇烈，應收取最高之保證金；金融期入波動性次之，保證金水準稍低；臺股期貨波動性最小，應收取最低之保證金水準。此一結果與目前市場的實際狀況頗為吻合。 由於臺灣期貨市場有7%價格漲跌停限制，本文依照Brousard (2001)之研究方法，以每天期貨最大值減結算價、最小值減結算價分別計算空頭及多頭部位持有者，在6%與7%價格限制下，以極值理論求取不同違約機率下之保證金水準。實證結果發現在6%價何限制條件下，期貨保證金水準應較7%價何限制條件之保證金為低。

This paper is aimed to apply the extreme value theory to estimate the appropriate margin levels of the futures market in Taiwan. The weighted stock, financial sector stock and electronic sector stock index futures have been chosen and analyzed in this study. Methodologically, the Gauss-Newton method is utilized to estimate the parameters in the nonlinear regression. Statistically, a small sample size might not satisfy the property of probability limit on finding the distribution of extreme values. In addition, it will also reduce the accuracy on estimating the parameters in this model. In order to overcome these problems, we made use of the 5-minute-transcation intra-day data to set the margin levels for the three index futures. Six different trading periods (n), corresponding to six different extreme value samples have been created and studied in our empirical study to estimate the reasonable trading periods (n) for the three different futures contracts. The findings of this paper include: the electronic sector and the financial sector index futures have the largest and smallest volatility, respectively. Under the same probability of default, the margin level of electronic sector index futures should be larger than financial sector index futures. In fact, these findings are quite consistent with the observations in the market. Furthermore, due to the limitations of 7% price variation, the method proposed by Brossard (2001), which is based on different probabilities of default and different percentages of price limitation has been used to find the appropriate futures margin level. The conclusion is that the estimated futures margin level with 6% price limitation should be set lower than the one with 7% limitation.