The Margin Levels Setting in Taiwan Futures Market

[[abstract]]本文應用極值理論研究台股指數期貨報酬之極值行為與保證金水準之估計。在極值理論的應用上，本文主要採取無母數方法以避免有母數方法在估計時必須對於分配作假設之限制。此外，本文除了以Hill法估計保證金水準之外，更進一步引進VaR-x法於保證金水準的研究上，以解決Hill估計式在小樣本下的偏誤。本文研究期間為1998年07月21日至2001年11月9日。本文實證結果為：1.台股指數期貨價格變動符合Frechet極值分配。2.常態分配的假設會造成保證金水準的低估。3.在小樣本的情況下，Hill估計式會造成保證金水準設定的偏誤，而本研究所引進的VaR-x法則可成功的修正此缺點，並且VaR-x法可提供期交所在設定保證金水準時，一個非常簡便而且可以滿精確計算保證金水準的方式。4.在考量不同部位風險程度的情況下，期交所應設定不同之保證金水準。5.進行動態風險管理時，較建議採用EGARCH模型。由於每日設定不同保證金水準在實務上並不易實施，因此建議當報酬波動達到某一程度時才重新設定保證金水準，在進行動態風險控管時較符合實際情況。[[abstract]]This paper examines the behavior for TAIFEX weighted stock index futures contracts, and applies extreme theory in computing optimal margin levels for TAIFEX weighted stock index future. In this paper we use the Hill estimator of nonparametric approach in computing margin level, because it do not assume distribution that the observations of extremes follow exactly the asymptotic distribution. Furthermore, we apply the VaR-x method for correcting the bias errors in small sample of Hill index. The sample period is from July 21, 1998 to November 9, 2001. In our empirical findings, we get that: (1) TAIFEX weighted stock index future price changes follow a Frechet extreme value distribution, (2) the comparison of the extreme value method with a method based on normality shows that using normality leads to underestimates the margin level, (3) Hill index leads to dramatic overestimates of the margin level, and VaR-x avoids this problem, (4) there are significant differences between the risk inherent in long and short position, TAIFEX should impose different margin level. (5) the result show that EGARCH model provides a more accurate margin level for dynamic risk measurement than GJRGARCH model