使用真實波動度交易於臺指選擇權的經濟價值

Abstract

本文使用真實波動度模型，研究台灣股價指數選擇權市場的資訊內涵，我們比較預測期間為一天到五天的臺指選擇權的真實波動度的預測模型，其中真實波動度的計算方式採用日內的交易資料。使用隱含波動度、歷史波動度、GARCH(1,1)和ARFIMA等四種模型分別討論其對真實波動度的解釋、預測能力。其中ARFIMA模型能描繪真實波動度的緩長記憶效果。 欲比較各模型對真實波動度的解釋、預測效果，本文使用三種方式：1.均方根誤差(root of mean squared error, RMSE)。2.單一迴歸式檢定各個預測模型的係數是否顯著異於零，且比較R2值。3.利用包含迴歸式檢定在自變數為隱含波動度時，若再增加一自變數，檢定此增加的參數是否會顯著提升對真實波動度的包含資訊：研究發現ARFIMA模型在當期、預測一天和預測五天的包含迴歸式中的係數都相當顯著，表示其對真實波動度有額外的解釋、預測能力是隱含波動未包含的資訊。 最後，驗證對樣本外(預測未來一天)真實波動度的預測值，比較各個模型是否能在本文使用的交易策略於臺指選擇權市場中獲利。研究發現當未考慮交易成本前，GARCH、ARFIMA模型可得到平均每天2.01%、2.53%的報酬，若考慮交易成本後，GARCH、ARFIMA模型可得到1.75%、2.27%的報酬。利用夏普指標分析方面，結果顯示在未考慮交易成本時，GARCH、ARFIMA模型的投資績效較市場好，在考慮交易成本後HV的投資績效亦較投資於大盤市場佳。

This research is to investigate the information content in TAIEX options market by using the “realized” volatility approach. We compare forecasts of the realized volatility of the TAIEX options, calculated from intraday data, over horizons ranging from one day to five days. Our forecast models obtained from a historic volatility, a GARCH(1,1) model, a long memory ARFIMA model and option implied volatilities. To compare forecasts of the realized volatility, we use three ways as follow: 1. Root of Mean Squared Error. 2. Simple regression to tell whether the coefficient of each model is significant non-zero and compare the R2 value. 3. Encompassing regression to analyze whether the information content in the forecasted volatility model is subsumed in the implied volatility forecast. In our research, we find that no matter the coefficients of ARFIMA model in current day, forecast one-day-ahead or five-day-ahead are significant different from zero. It shows that ARFIMA model has excess information content in the forecasted volatility model is not subsumed in the implied volatility forecast. Finally, in order to evaluate the economic benefits of volatility timing, we need to tell whether realized volatility forecasts can be used to formulate profitable out-of-sample trading strategies in TAIEX options market or not. The answer is that the volatility timing has positive returns of 2.01% and 2.53% per day before considering trading cost when we using GARCH model and ARFIMA model. After considering trading cost, the returns became 1.75% and 2.27%, but the values are also not robust.