在期貨與現貨市場間,考量交易成本的存在,市場會產生無套利區間,唯有當價差超出無套利區間,扣除交易總成本後有淨獲利時,才會出現套利活動,產生均值回復(mean reversion),使期貨與現貨市場動態調整而達長期均衡狀態。過去研究指數期貨與現貨兩市場間的關聯性時,大多強調市場價格發現功能與領先落後關係,且多以線性模型分析期貨與現貨市場的交互動態關係。 本研究以「臺灣證券交易所股價指數」、「臺灣證券交易所電子類股價指數」與「臺灣證券交易所金融保險類股價指數」期貨與現貨日報酬率為資料,使用McMillan(2001)所提出外生平滑轉換自我迴歸模型(smooth transition autoregressive exogenous,STARX),探討期貨與現貨間,是否較適合以非線性模型描述其關連性,以及兩者間的非線性調整行為。 從本研究的實證結果可以觀察到以下結論: (1) 三者間皆拒絕線性的虛無假設,表示三者間存在非線性調整行為,且均通過 ESTARX 模型的估計;(2) 在不同指數的報酬下,其顯著的外生變數落後期和轉換變數落後期不盡相同的,表示可能由於構成指數之成分股的特性差異,會有不同的變數遞延效果;(3) ESTARX 的估計結果顯示,模型的轉換門檻值大小依序為:金融指數>電子指數>台股指數,比照過去的歷史交易金額與市值比重上發現,當現貨與期貨市場產生報酬率差異時,交易愈活絡、流通量愈大的市場,有較高的套利動機,進行套利的要求門檻值報酬率較低。
If we consider the trading costs between futures and spot market, an arbitrage-free regime would exist between the markets,only when price margin exceeds the arbitrage-free regime and profited after net the total transaction cost. The arbitrage activities and the mean reversion would come into existence and the dynamic adjustment between futures and spot market also come into a long-term balance. Most of the conventional surveys of the relations between index future and spot market emphasized on the price discover function of the lead and lag relationship, in addition, most relations of interactions and dynamics between future and spot market were analyzed by linear module. The return rate data of future and spot market in this dissertation were from “Taiwan Stock Exchange Weighted Index”, ”Taiwan Stock Exchange Electronic Sector Weighted Index ” and “Taiwan Stock Exchange Financial Sector Weighted Index”. By using the smooth transition autoregressive exogenous (STARX) which argued by McMillan (2001) discussing whether the linear model is more suitable to describe the relation between future and spot market, and their non-linear adjustment bahavior. The following conclusions can be observed by empirical results of this dissertation. 1) They all reject the null hypothesis. It represents the non-linear adjustment activities existed within them three and also pass the estimate of the ESTARX model. 2) Under different index profits, it’s obvious that lags of the exogenous variables and the convert variables are not extremely the same, it reveals the differences between constituent of indices may have different effects on deferred variable. 3) According to the results of ESTARX estimate, the height sequence of model transfer barriers is “Financial index > Electronic index > Taiwan stock index”. On the other hand, comparing to the historical transaction amount and market share, it can be observed that when the profit rate in future and spot market has discrepancy, the market which has more active trading and more circulation owns higher motivation of arbitrage, and also lower arbitrage return value under required threshold.
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