漲跌幅限制與極值理論在期貨保證金設定上之應用

Abstract

極值理論近來常應用於期貨的保證金比例之設定，然而期貨漲跌幅限制可能影響極值分配的估計結果，文獻在這方面尚未有完整研究。本文目的即在於分析漲跌幅限制的影響，並以台灣期交所的台指期貨，與新加坡期交所的摩根台指期貨市場資料進行實證。結果發現，漲跌限制截斷了期貨日內價格變化的極端行為，因此報酬率分配的峰態減緩，對極值分配的參數估計、保證金不足的機率估計與保證金比例設定均有影響。尤其是摩根台指期貨的7%漲跌幅限制，設置在日內價格變化的極端位置上，因此有較顯著的影響。此外，期貨漲跌幅限制與保證金對於降低期貨價格波動性有替代效果。較窄小的漲跌幅限制可以降低期貨價格的波動性，有助於控制期貨的違約風險，因此只須相對要求較低的期貨保證金比例。這個結果可以解釋為何台灣期交所與新加坡期交所設定的保證金比例低於理論值，因為它們都搭配了價格限制機制。

Extreme value theory has recently been applied to margin setting in futures markets. Price limits, however, may undermine the benefits associated with the extreme-value method. This has not to be accomplished in the literature. The purpose of this article is to examine the impacts of price limits on the results of extreme value parameter estimation. Both index futures in Taiwan Futures Exchange and Singapore Exchange are used as samples. The results indicate that price limits impede the extreme price behaviors, and the excess kurtosis of distribution become less significant. Besides, the price limits may affect the tail parameters, default probability, and margin ratios estimation. Especially, because the 7% price limits in Singapore Exchange are set in the positions of extreme values, they imply more significant impacts. Price limits may also substitute the function of margins in the sense of lowering the price volatility by impeding the extreme price change directly. This explains why both Taiwan Futures Exchange and Singapore Exchange set the margin ratios lower than theatricals ratios.