台指週選擇權價差交易之實證分析

Abstract

本文擬藉由蒐集到的台指選擇權一週到期契約（以下簡稱台指週選）統計資訊，用以研究時間價值價差交易策略，是否有正報酬的可能。 本研究擬採的價差交易策略是指，以最接近價平履約價的選擇權（Omiddle）及其上下三檔的選擇權中，建構下列四組組合部位 組合部位 買 賣 買權價內部分 "時間價值"最低的價內買權 "時間價值"最高的價內買權 買權價外部分 "時間價值"最低的價外買權 "時間價值"最高的價外買權 賣權價內部分 "時間價值"最低的價內賣權 "時間價值"最高的價內賣權 賣權價外部分 "時間價值"最低的價外賣權 "時間價值"最高的價外賣權 註：當"時間價值"一樣低時，買入市價低的選擇權。 當"時間價值"一樣高時，賣出較價內的選擇權。

本研究主要有以下發現： （一）雖然週選擇權，深度價內的選擇權價格，高於淺度價內選擇權價格，但深度價內選擇權的所含的"時間價值"較低的現象。

（二）就第一點的現象，同時建立四組組合部位並週期性的建立，扣除交易成本後，仍有機會取得正報酬。

（三）就第一點現象進一步觀察，在台灣指數一天之內波動100點時，雖然Omiddle（最接近價平履約價的選擇權）會跟著改變，例如由9000點移動致8950點，但"時間價值"自Omiddle向兩側遞減的現象仍然存在（本研究稱小山現象，Montanita phenomenon ）。

（四）就第三點小山分配，Omiddle及其上下三檔選擇權的時間價值，在一定期間內，相對穩定，似可利用「選擇權價值=內含價值+＂時間價值"」來評估選擇權的可能市價。

Through the date of TAIEX Weekly Options, whether it is possible to profit under the "time value" spreading. The "time value" spreading is that building four positions among the Omiddle and the 3 options with the deeper strike price and the 3 options with the deeper strike price (the Omiddle is the option with the strike price most close to the at-the-money price) Postion Buy Sell ITMCall Call with the min TV Call with the max TV OTMCall Call with the min TV Call with the max TV ITMPut Put with the min TV Put with the max TV OTMPut Put with the min TV Put with the max TV Note：When two(or more) options have the lowest "time value"，buy the option with the lowest premium. When two(or more) options have the highest "time value"，sell the option with the highest premium.

This thesis finds the followings： 1. Although the deeper in-the-money, the higher premium; the option deeper in-the-money have lower time value. 2.Based on the above finding, it is possible to make profit when routinely building four positions at the same time and with the consideration of transaction cost. 3.When TAIEX change 100 points during a trading day, though the Omiddle will change , Montanita phenomenon ,which means the distribution of that time values of the 7 options mentioned is shaped like "small mountain", still exists. 4.According to Montanita phenomenon, time values of the 7 options mentioned above are quite stable during a period of time, therefore the function " option value = intrinsic value + time value" may be used to predict the premium of the options.