選擇權市場效率性檢定：隱含波動率成對交易檢定法

Abstract

由於台灣股票市場中電子類股佔整體市場約70%的成交比重，因此電子指數與台股加權指數間應存在共同的波動率因子，以兩者為標的之選擇權的隱含波動率差亦應存在一長期穩定關係。本文檢定台指買權及電子買權隱含波動率序列是否存在共同因子，並檢定兩隱含波動率序列是否存在緩長記憶性；接著，以均數回歸模型檢定兩選擇權隱含波動率差偏離均衡後的動態行為；最後，使用成對交易進行選擇權市場交互效率性檢定。此檢定法的特點是以選擇權波動率差偏離幅度設計交易策略，因此只需觀察選擇權隱含波動率的相對偏離程度，不需選擇權的合理價格。在交易策略的設計方面，除過去文獻提出的交易策略外，我們另提出一以波動率差的均數回歸速度決定持有期間的持有期間判斷準則。實證資料顯示，台指買權及電子買權隱含波動率序列確實存在共同因子，且兩選擇權的隱含波動率序列存在長期穩定關係、隱含波動率差序列則呈現均數回歸過程。以波動率差為進出場訊號建構投資組合，在考量保證金及交易成本後發現建構投資組合的次數不多，且平均報酬率雖為正但並不顯著。這些結果顯示台指買權及電子買權出現相對錯誤定價的機會不高且針對錯誤定價建構的模擬投資組合無法帶來顯著正獲利。台灣選擇權市場中台指買權與電子買權的定價具有交互效率性。

Based on the fact that the market capitalization of the electronic sector often accounts for about 70% of the total market capitalization of the Taiwan stock market, we consider if there exist a common volatility factor and a long-run stable relationship between the electronic sector index and the Taiwan Stock Exchange capitalization weighted stock index and, therefore, between the implied volatilities of the options contracts, whose underlying indices are the electronic sector index and the Taiwan Stock Exchange capitalization weighted stock index, respectively. In particular, in order to examine such a conjecture, this paper firstly tests whether the implied volatilities posses the property of long memory and a common volatility factor. Secondly, we construct a mean-reverting regression model to capture the dynamic behavior of the spread between the implied volatilities. Finally, we investigate the cross-market efficiency of the index options market in Taiwan according to the pair trading strategies of volatility spread. By utilizing the pair trading strategies, we can avoid calculating the daunting fair values of options contracts and just focus on the spread of implied volatilities. In addition to the strategies studied in the literature, we also design a pair trading strategy, which is based on the speed for the volatility spread to revert to its long term mean, to study the cross-market efficiency of the index options market in Taiwan. The empirical results show that there exists a common factor and a long-run stable relationship between the implied volatilities of the two index options contracts and that the dynamic behavior of the volatility spread follows a mean-reverting stationary process. Regarding the test of cross-market efficiency, we find that after taking the margins and transaction costs into account, the options portfolios constructed based on the volatility spread do not trade much and deliver only insignificant profits. Overall, these results suggest that there does not exist significant pricing error between the options contracts of the electronic sector index and the Taiwan Stock Exchange capitalization weighted stock index and the pair trading strategies based on the spread of their implied volatilities would not bring investors significant profits. Therefore, there exists cross-market efficiency for the index options market in Taiwan.