| Abstract: | 選擇權訂價模型中，波動性的估計是重要探討之議題，學者專家們相繼提出各種波動性之估計模型，欲尋找出何種波動性模型所得之選擇權理論價格與實際市場價格差距最小，本文中以台灣加權股價指數及台灣股價指數選擇權為研究標的，利用變幅估計式（Range Based Estimators）估計其波動性，結合採用不對稱GJR-GARCH模型及MA、AR、EWMA、RW及ARMA等時間序列模型等作為預測模型，並以平均絕對誤差（mean absolute errors， MAE）、均方誤差（mean squared errors，MSE）、平均混合誤差（mean mixed error，MME）等傳統損失函數及優勢預測能力檢定（Superior Predictive Ability Test，SPA）模型，來衡量不同方法模型中何種模型預測績效較能貼近實際市場波動性，希望能藉此找出一適合的模型，可較準確地預測出台灣股價指數波動度，藉以降低台指選擇權之交易風險。結果顯示結合變幅估計式之預測模型對於台灣加權股價指數有較佳的預測效果，而對台灣股價指數選擇權，則以GJR-GARCH模型預測效果較佳。
On the field of the option pricing model, the prediction of volatility is one of the important topics among others. For the purpose of searching for a model reflecting the narrowest gap between the theoretical prices of option and the actual market price, the scholars and experts have proposed a variety of models for volatility prediction. This article takes TAIEX and TAIEX Option as the research object, using Range-Based Estimators to estimate the volatility, along with asymmetric GJR-GARCH model and the MA, AR, EWMA, RW and ARMA time series model as the models for the prediction of TAIEX and TAIEX Option. Furthermore, some traditional loss function such as mean absolute errors, MAE, mean squared errors, MSE, and mean mixed errors, MME as well as the Superior Predictive Ability Test, SPA are applied in this article to determine which model with the foregoing methods has better accuracy in predicting the volatility of the actual market. In addition, the goal of this article is in a hope to search out a proper model which can predict the volatility of TAIEX more accurately, and to reduce the transaction risk of TAIEX Option by way of such model. In conclusion, the result indicates that the combination of Range-Based Estimators of the predicting model presents a better effect on prediction for TAIEX, while GJR-GARCH is better for TAIEX Option. |
