台灣指數選擇權隱含波動率曲面變動影響因子之研究

Abstract

本研究利用主成份分析法及複迴歸分析，找出市場變數對台指選擇權隱含波動率之影響，在第一部分是將隱含波動率依照到期期間長短及涉價比率高低兩個標準分為九個區間，利用主成份分析法找出隱含波動率的變動因子，實證結果發現，買權契約的第一個主成份為「短期選擇權之隱含波動率」，而賣權契約的第一個主成份為「短期選擇權及中期且價外選擇權之隱含波動率」，此外，買權及賣權的第二個主成份分別為「長期且價內選擇權之隱含波動率」及「中期且價內選擇權之隱含波動率」。 第二個部份是以短期選擇權之曲面代表點的變動為應變數，其它三個市場變數(大盤交易量、大盤指數及虛擬變數)為自變數，利用迴歸分析找出市場變數與短期選擇權之關係。實證結果發現買權契約之隱含波動率，與大盤交易量呈現正相關，而虛擬變數在所有的涉價比率下也都呈現正相關，且虛擬變數會隨著涉價比率從價外到價內，變得愈來愈顯著；賣權契約在所有涉價比率下的隱含波動率，與大盤交易量及虛擬變數並不顯著，與大盤指數則為顯著負相關，而且隨著涉價比率從價外到價內，與大盤指數的關係變得愈來愈顯著。

This paper adopts the principal component analysis (PCA) and regression analysis to find out how the market variables can affect the implied volatility in TXO. In the first part, the data is divided to 9 sections with different maturity and moneyness. The result from PCA shows that the first component explaining implied volatility changes in calls is implied volatility of short-term options, and the first component in puts is implied volatility of short-term options and medium-term out–of-the-money options. The second component in calls and puts is implied volatility of long-term in-the-money options. The third component in calls and puts is implied volatility of medium-term in-the-money options. In the second part, the empirical result indicates that the implied volatility in calls is positively related with the market volumes and dummy variable in all moneyness. Meanwhile, the implied volatility in puts is negatively related with the stock index. And this relationship is more significant for out-of-the-money than that of in-the-money options. No significant relationship is found between the market volume and all moneyness variables.