應用期望到期報酬及數學優勢模型於篩選與建立最佳選擇權組合交易策略

On Screening and Creating the Optimal Option Combination Strategy Using Expected Final Return and Mathematical Advantage Models

10.6626/MR.201912_19.0002

黃明官(Ming-Guan Huang)；黃啟倉(Chi-Chang Huang)；賴玉珮(Yu-Pei Lai)

選擇權組合策略 ； 數學優勢模型 ； 期望到期報酬模型 ； 台指選擇權 ； combination strategy ； expected terminal return model ； mathematical advantage model ； TAIEX options

管理研究學報

19卷（2019 / 12 / 01）

31 - 69

繁體中文

近年來金融數學與財務計量方法廣為發展與實際應用，特別是應用在像選擇權之類複雜的金融商品。事先可藉助計量方法求得其最可能結果，並將結果運用於篩選出最佳獲利潛力的交易策略，數學計量方法的有效性並非尋求每次獲利而是長期交易中穩定獲利。本研究首先運用機率與數學期望值概念與方法，推導出選擇權賣出跨式及勒式策略的期望到期報酬模型及數學優勢模型。其後，再將此兩模型應用於作為建立每期具有潛在最大獲利能力的賣出組合策略的篩選指標。最後，本研究利用短天期之週到期台指選擇權作為實證研究樣本，實證研究期間自2013年至2017年，總計執行249期（週）之實證研究。同時，本研究於各測試期中皆選取價平一檔、最近價內三檔及最近價外三檔，並從中組合出共7組賣出跨式策略及21組賣出勒式策略，透過大規模實證藉以驗證本研究所發展之計量模型的有效性、實用性與獲利性。實證結果顯示，本研究所發展與建議的兩種計量模型對於到期實際報酬確實具有相當優異的預測能力與篩選能力，而期望到期報酬模型的整體預測能力優於數學優勢模型。此外，視窗30日波動率略較視窗91日及視窗182日精確，同時，採用兩種計量模型之最佳策略獲得的投資績效皆明顯優於固定履約價格策略，另外，最佳期望到期報酬策略平均而言每期可獲得可觀的投資報酬率。因此，相信本研究之研究成果與實證發現應可以提供給學術界及實務界一定之參考價值。

In recent years, financial mathematics and financial quantitative measurements have been widely developed and applied. These techniques are particularly applicable to such complicated financial products as options. The most probable results may be obtained in advance by means of quantitative methods. Then, these results can be used to screen out a trading strategy, which has the best profit potential. The effectiveness of the mathematical quantitative approach is not to earn each time but seek a long-term stable gain. This study firstly deduces the expected terminal return model and mathematical advantage model for option' short straddle and strangle strategies by making use of the concept and method of probability and mathematical expectation. Secondly, these two models are taken as the screening criteria that create the optimal short combination strategy with a potential maximum profitability. Finally, this study takes short-term weekly Taiwan weighted stock index options (TXO) as example to conduct a long-term large-scale empirical study. The empirical study ranges from January 2013 to October 2017, and covers in total 249 empirical periods. In the meantime, in each empirical period, this study selects one at-the-money option, three nearest in-the-money options and three out-the-money options, and thus makes up the groups of 7 short straddle strategies and 21 short strangle strategies respectively. This large-scale empirical study is performed for the purpose of verifying the accuracy, practicability and profitability of quantitative modes developed in this study. The empirical results show that the two quantitative models developed and proposed here do have excellent predictive and screening ability for the actual terminal returns. Moreover, the predictive ability of the expected terminal return model is superior to the mathematical advantage model. Additionally, window 30-day volatility is slightly more accurate than window 91-day volatility and window 182-day volatility. Also, the investment performance obtained by using the best strategies derived from the two quantitative models is obviously better than the fixed exercise price strategy. Also, the optimal expected terminal return strategy can acquire on average a considerable rate of return during a trade. Therefore, this study is confident that the research works and empirical findings in this study should be able to provide a reference value to the academic and practical sectors.

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