台股期貨與摩台指期貨之時間價差行為模式之套利研究

Abstract

契約到期日不同一直是台股期貨與摩台指期貨間執行跨市場套利的難題。然而從時間價值的角度來思考，到期日的不同會產生不同的時間價值衰退現象，使得標的期貨間出現時間價值價差。到期日的不同反而成為套利的利基。本論文發展以選擇權為基礎之期貨套利策略（OBFA），利用Black-Scholes模型計算各期貨對應之虛擬期貨選擇權做為標的期貨時間價值之分析指標，並綜合台指基差與摩台指基差之條件分析，評估套利機會發生的可能。本研究使用台股期貨與摩台指期貨之分鐘資料執行OBFA交易模擬實證，實驗資料之歷史期間自2001年1月1日至2003年1月31日。 研究結果顯示台股期貨與摩台指期貨間存在時間價值價差的套利機會，並且發現最佳的套利機會發生條件狀態以及交易策略為： （1） 台指基差為正，摩台指基差為負，時間價值價差小 月初當台指與摩台指間基差之差距達1.009％以上，同時兩期貨間時間價值價差出現縮小現象時，做空台股期貨並做多摩台指期貨，而後於台股期貨最後交易日前平倉實現損益。每筆套利交易的報酬率期望值為2.18％，報酬率之變異數為0.47％。 （2） 台指基差為負，摩台指基差為正，時間價值價差小 月初當台指與摩台指間基差之差距達0.802％以上，同時兩期貨間時間價值價差出現縮小現象時，做多台股期貨並做空摩台指期貨，而後於台股期貨最後交易日前平倉實現損益。

The mismatch of maturity date between Taiwan Stock Index Futures (TX) and MSCI Taiwan Stock Index Futures (STW) would vary the time value between the two futures and course that arbitrage opportunity occurs in between. In order to explore the arbitrage opportunities of time spread, an Option Based Futures Arbitrage (OBFA) model is developed in this thesis. In the OBFA, the Black-Scholes model is employed to calculate the virtual futures options for TX and STW as analysis indices of time value. Combining with the situation analysis of Taiwan Stock Index basis (T-basis) and MSCI Taiwan Stock Index basis (S-basis), OBFA would be used to discovery the conditions which arbitrage opportunities occur on. 1-minute tick data of TX and STW are used in the OBFA trading simulation experiment. The historical period of experiment data is from 2001/1/1 to 2003/1/31. It is shown by the simulating experiment that there are arbitrage opportunities of time value spread between TX and STW. It is also found in the experiment that the best conditions of arbitrage opportunities and the trading strategy are: 1. T-basis is plus, S-basis is minus, and the time value spread is small In the beginning of month, if the spread percentage between T-basis and S-basis is more than 1.009% and the time value spread between TX and STW is small, then the strategy of longing TX and shorting STW is executed. Finally, both futures should be offset before the last trading date of TX. The expected profit is 2.18%, and the variance of the profit is 0.47%. 2. T-basis is minus, S-basis is plus, and the time value spread is small In the beginning of month, if the spread percentage between T-basis and S-basis is more than 0.802% and the time value spread between TX and STW is small, then the strategy of longing TX and shorting STW is executed. Finally, both futures should be offset before the last trading date of TX.