本研究鑑於八十六年一月上市的摩根台股指數期貨，市場價格與理論價格發生頗大幅度的乖離，故以日成交量資料綜觀此市場實際狀況後，擷取最近月和部份次近月的五分鐘資料進行實證研究。

考量借貸利率差異和我國證券市場融券保證金制度，將產生不同的期貨理論價格，加上交易成本建構出無套利機會區間，再考慮風險溢酬後設定無套利執行區間。利用二次規劃模型以累計追蹤誤差最小化為目標式，求得最適指數模擬投資組合，依此進行指數套利交易。

研究結果摘要如下：

一、樣本期間二十一個期貨合約的市場價格，並不符合持有成本模型下的理論價格，有十八個期貨合約價格顯著偏低。

二、總樣本僅有48.9%落在具效率的無套利機會區間中，20.2%低於無套利執行區間下限，可進行融券放空股票買入期指的反向套利；有0.7%高於無套利執行區間上限，可進行買入股票賣出期指的正向套利。

三、反向套利執行機會持續期間平均1.1小時，最長高達20.8小時；正向套利平均持續期間為22.7分鐘。套利部位平均存續期間為15.1日。

四、平均套利利潤為2.26%，反向套利最大利潤高達11.55%，正向為4.42%。第一類交易者模擬套利交易一年的報酬率為25.43

五、以第二類交易者成本進行模擬組合套利交易七回合，累計一年的報酬率為22.39%。模擬期間平均累計追蹤誤差0.23%、匯率誤差值－0.07%，期貨保證金追繳機率為6%。

第一章 緒論 ……………………………………………… 1

第一節 研究背景與動機 …………………………… 1

第二節 研究目的 …………………………………… 3

第三節 研究範圍與架構 …………………………… 4

第二章 文獻探討 ………………………………………… 7

第一節 無套利條件 …………………………………… 7

第二節 持有成本模型下的價格偏誤 ……………… 17

第三節 市場組合的建構 …………………………… 20

第三章 研究方法與資料整理 …………………………… 24

第一節 樣本期間與資料來源 ……………………… 24

第二節 指數期貨合約定價模式 …………………… 27

第三節 相對價格偏誤的衡量 ……………………… 31

第四節 建構無套利區間 …………………………… 32

第五節 建立模擬組合 ……………………………… 35

第四章 實證結果與分析 ………………………………… 41

第一節 期貨的價格偏誤 …………………………… 41

第二節 期貨的無套利區間 ………………………… 45

第三節 模擬套利交易 ………….…………………… 61

第五章 結論與建議 …………………………………… 100

第一節 結論 …………………………………………… 100

第二節 研究限制與未來研究建議 ……………… 102

參考文獻 ………………………………………………… 103

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This paper is induced by the serious mispricing of MSCI Taiwan index futures,listed in January 1997. The empirical evidence is based on five minutes intraday data of nearby and far nearest futures contracts.

There are different theoretical futures prices as the risk-free borrow-ing and lending rate are different and concerning our securities market short selling rules.We build the no-arbitrage opportunity bounds and the no-arbitrage trading bounds after added trasaction costs and risk premium. We get the optimal mimic portfolio to pull the trigger by using the quadratic programming which minimizing the accumulative tracking errors.The important results are as follows：

1. The 21 futures contracts market prices of my sample period can not be described by the cost of carry model.The average size of mispricing is significantly different from zero.There are 18 futures contracts actual prices significantly underpricing.

2. There are only 48.9% intraday observations efficiently priced within the no-arbitrage boundaries.It existed 20.2% observations under the no-arbitrage trading lower bounds to trigger short arbitrages and 0.7% observations over the higher bounds to trigger long arbitrages.

3. The average time of underpricing subsequent violations is 1.1hours and at the longest is 20.8 hours. The average time of overpricing subsequent violations is 22.7 mimutes.The average holding period of arbitrages position is 15.1 days.

4. The average arbitrage profits are 2.26%.The maximum profit of short arbitrages has reached 11.55% and long arbitrages reached 4.42%. We earn 25.43% returns from simulating arbitrage trading for one year

depending upon the category 1 traders.

5. Depending upon the category 2 traders,we simulate arbitrage trading by mimic portfolio and futures contracts for 7 rounds.The average of accumulative tracking errors is 0.23%,exchange rate errors is -0.07%, futures margin call probability is 6%.The total returns are 22.39% for one year.

中文部份：
王隆盛, 運用啟發式演算法於股價指數套利投資組合模式之建立,
交通大學資訊管理研究所未出版碩士論文,民國86年。
林文政、臧大年, 台股指數期貨定價與套利實務問題探討,國科會研究
計劃 NSC-84-2416-H-194-004 A3,民國85年。
李存修, 指數型基金,股價指數期貨與股票市場間的互動關係,證券分
析簡訊,民國83年。
吳雲龍, 台股指數套利研究,台灣大學財務金融學研究所未出版碩士
論文,民國87年。
陳其緯, 台股指數期貨套利之實證分析,台灣大學商學研究所未出版
碩士論文,民國86年。
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