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題名：台股指數期貨基差調整過程之探討─應用平滑轉換自我迴歸模式
作者：張瓊嬌
作者(外文)：Chiung Chiao Chang
校院名稱：國立臺北大學
系所名稱：企業管理學系
指導教授：古永嘉
學位類別：博士
出版日期：2003
主題關鍵詞：基差ANSTGARCH；均數返還；非線性；STAR；EGARCH；ANSTGARCH；basis；mean reversion；nonlinear；STAR；EGARCH；ANSTGARCH
原始連結：連回原系統網址new window
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由於基差的變動會直接影響避險、指數套利者的操作績效，對市場價格的發現與資訊的傳遞亦有重要的影響力。然而文獻上對於期貨市場的探討主要偏重於兩個方向，一為期貨與現貨兩市場間的領先落後關係，二為期貨錯價的研究，對於期貨基差本身的研究較不足，故本研究以TAIFEX與SGX兩期貨交易所所推出以台股指數為標的物之期貨契約的基差行為作為研究對象，研究樣本期間為87年7月21日至91年12月31日間現貨與近月期貨合約的每日收盤價與結算價。
在完美的資本市場、固定的利率與股利支付率的假設下，基差的變動具有線性均數返還特質，亦即基差變動的速度是固定的。然而當存在交易成本的不完美的資本市場時，期貨價格會出現所謂的無套利區間，繼而使期貨基差的變動存在無套利區間，此時基差變動具有顯著的非線性特質。當期貨價格偏離均衡價格愈遠(超過無套利區間)時，基差呈現強烈的均數返還的現象；但是當期貨價格偏離均衡價格的程度較小時(位於無套利區間內)，基差呈現單根的現象。若主導期貨期差的過程是非線性，那麼採用傳統線性模式可能無法完全捕捉到期貨基差的所有行為。因此本研究藉由非線性模式STAR、EGARCH與ANSTGARCH模式探討兩市場期貨基差是否具有非線性均數返還、波動不對稱與波動的平滑轉換的特質，希望能藉由本研究補足目前相關研究上的缺口。
研究結果發現：首先兩市場基差變動以線性模式AR(3)配適後，採用RESET檢定與Teräsvirta (1994)線性檢定皆顯示兩市場基差變動存在非線性特質。其次，TAIFEX市場期貨基差變動對於正偏離與負偏離具有對稱性反應，描述TAIFEX市場之基差調整行為的最佳模式為ESTAR，延遲期數等於5；但SGX市場則呈現不對稱現象，描述其基差調整行為的最佳模式為LSTAR，延遲期數等於5。第三，TAIFEX市場基差調整在無套利區間內未具有單根性質，仍存在均數返還的性質；SGX市場基差在上下兩個極端區間皆呈現強烈均數返還的恆定現象，但無法檢視在無套利區間是否具有單根性質。另外，由轉換速度參數發現，SGX市場的轉換速度參數比TAIFEX市場高，顯示前者投資人所面臨的交易成本的同質性比後者高。第四，TAIFEX市場期貨基差變動具有波動不對稱現象，可以EGARCH(1,1)加以有效解釋：SGX市場除了具有波動不對稱外，更具有條件變異數區間平滑轉換的特質，可用ANSTGARCH(1,1)模式解釋。當考慮了條件變異數後，TAIFEX市場投資人所面臨的交易成本的同質性提高了，但SGX市場投資人所面臨的交易成本的同質性卻降低了。
To date, empirical research has focused either on lead-lag relationships between stock and stock index futures markets, or the behavior of mispricing. Although the basis change will directly affect the performances of hedge and index arbitrager, also have important effect on the price discovery and the information transmission. There are few literatures to investigate the futures basis itself. This paper investigates the behaviors of basis Change of the Stock Index Futures Traded in the TAIFEX and SGX.
Under the assumptions of perfect capital market, the basis changes exhibit linear mean reversion. When there exists market frictions, e.g. transaction costs, short selling restrictions, the basis changes contain nonlinear property. In the absence of transaction cost, deviations of the basis away from zero in either direction will trigger arbitrage. The transaction costs create a no arbitrage band or regime for the basis, but the basis can stray beyond the bounded. The basis should become increasingly mean reverting with the size of the deviation from the equilibrium level. For small deviations the basis may be characterized by unit root behavior, but for larger deviations the process is mean reverting. By allowing for heterogeneous transaction costs, this may leads to a smooth transition between regimes. This paper will adopt the nonlinear STAR model, EGARCH model, and ANSTGARCH model to capture the nonlinear mean reversion, the asymmetric volatility and time varying volatility which were also suspected existed in the process of the basis change.
These findings reveal that the basis of the two markets show strong evidence of non-linearity property. The basis change of the TAIFEX market is symmetric to positive deviation and negative deviation, and can be explained by the ESTAR model. The basis change of the SGX market is asymmetric to positive deviation and negative deviation, and can be explained by the LSTAR model. Although the degree of mean reversion in the basis is increasing with the size of the deviation from the equilibrium level, within the transaction costs band, the unit root hypothesis is not supported for the basis changes of the two markets. The degree of homogeneous of transaction costs that the investors of the SGX markets face is higher than the TAIFEX. The volatility of the basis change of the TAIFEX is asymmetric and can be captured by the EGARCH(1,1). The volatility of the basis change of the SGX is asymmetric and time varying, which can be explained by the ANSTGARCH(1,1).
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