預測股價指數波動率－－新VIX與長期記憶模型之比較

Forecasting Stock Index Volatility: A Comparsion between New VIX and Long Memory Model

本文旨在比較不同波動率模型預測能力之優劣，文中以ARFIMA為長期記憶時間序列模型的代表，並輔以ARMA及GARCH兩種短期記憶時間序列模型進行比較。另外，本文修正CBOE新推出的VIX計算方式後，建立一個適合臺指選擇權交易特性的TVIX，並以其為隱含波動率模型的代表。本文之實證結果顯示：預測範圍為一日、一週及兩週下，ARFIMA有最好的預測力；預測範圍為一個月時，TVIX的表現則最佳。若考慮同時採用時間序列與隱含波動率模型是否會比單一模型有更多資訊時，預測範圍為一日、一週及兩週下，短期記憶模型加上TVIX會有最好的預測力；預測範圍為一個月時，則單獨採用TVIX仍有最佳的預測績效。

The main purpose of this paper is to compare forcasts of the realized volatility of the Taiwan Stock Exchange Capitalization Weighted Stock Index Options (TXO). The forecasts of time series models are obtained from a long memory ARFIMA model and short memory ARMA and GARCH models. Besides, we construct TVIX modified from the CBOE’s new VIX to get the implied volatility. We find the ARFIMA model provides the most accurate forecasts for one-day, one-week, and two-week forecast horizons while the TVIX is the most exact one for one-day horizon. On the other hand, whether we can get better forecasts to use time series and implied volatility models at the same time than only each one of them? For one-day, one-week, and two-week horizons, we find a short memory model together with the TVIX provide the best forecasts. However, for one-month horizon, there is no incremental information in time series forecasts beyond the TVIX.