台指選擇權隱含波動率、偏態及峰態之資訊內涵

Abstract

實務上，選擇權價格所隱含之二階動差（即波動率）應用得非常普遍，但有關所隱含三階動差（偏態）及四階動差（峰態）之研究則較為少見。衍生性商品交易之主要經濟功能之一為“價格發現”，就選擇權而言，此一發現功能尚可擴及到其他母數。如果市場參與者尚未能發現這些資訊，那麼先佔者便會有資訊之優勢。 本研究即採用2005年各交易日的選擇權日內交易資料，利用Jarrow-Rudd模型及線性插補，萃取出每交易日選擇權所隱含28天的標準差、偏態及峰態，先探討分配的特徵，再利用迴歸模型，以實證的角度，檢定這些隱含動差對未來股價指數的解釋能力。所得之結論簡單歸納如下： 1. 選擇權隱含分配大致為右偏及低闊峰。 2. 隱含偏態及峰態，無論是個別或聯合而言，對於一天和一週後的股價指數皆具有顯著的解釋能力。 3. 在排除共線性的情況下，隱含波動率、偏態和峰態三者共同對於未來一天和一週的股價指數具有預測解釋能力；其中隱含波動率對於未來股價指數有正向關係，而隱含偏態及峰態兩者對於未來股價指數均呈現負向關係。另外，在此模型下，波動率對於股價指數預測的不對稱性並不顯著。 4. 在排除共線性的情況下，隱含偏態和峰態對未來一天和一週的隱含波動率亦有解釋能力，隱含偏態對於未來的波動率有負向關係，而隱含峰態則對於未來的波動率有正向關係。

Practically, the application of options implied second moment, implied volatility, is very popular, but the study of implied third moment, skewness, and fourth moment, kurtosis, is seldom. One of the main economic functions of trading derivatives is to “mine” the market price. With regard to options, the function of mining price can be extended to other parameters. If the participators in the market did not find such useful information, the first movers will be benefited by the information. This research uses the intraday data of Taiwan Stock Exchange Capitalization Weighted Index (TAIEX) call options of each trading day in 2005 and employs Jarrow-Rudd model and linear interpolation to extract 28-day implied volatility, skewness, and kurtosis. Then, use linear regression empirically to check the relation between options implied moments and the stock index one trading day and one week ahead. In substance, the conclusions are as follows, 1. Options implied distribution is positively-skewed and platykutic generally. 2. If we use implied skewness and/or implied kurtosis as independent variable(s), and the stock index some trading day(s) ahead as dependent variable, the model is significant. 3. Implied second, third, fourth moments together have good explanatory power to the underlying stock index one and five trading day(s) ahead. The asymmetry phenomenon that the rise or the drop of implied standard deviation will not significantly affect stock index. 4. Implied skewness and kurtosis together have explanatory power to future implied standard deviation.