Relationship between VIX and Stochastic Volatility

[[abstract]]本文探究股票市場波動度的資訊內涵，我們利用Javaheri（2005）以及Zhang and Zhu（2006）來估計股票市場隱含波動度及選擇權市場隱含波動度，並與歷史波動度及波動度指數進行分析比較。實證結果指出，美國市場資料顯示波動度指數比歷史波動度具有更好的解釋能力，而台灣市場資料顯示歷史波動度的解釋能力比波動度指數來的好。然而，研究結果也顯示在美國市場中，來自選擇權的隱含波動度對於真實波動度有著較好的解釋能力，而在台灣市場則發現股票市場的隱含波動度的解釋能力較好。但無論是在美國市場資料或者台灣市場資料中，隱含波動度比非隱含波動度可以估計更多資料的訊息。[[abstract]]This study investigated the information content of volatility in the stock market. We used the approach of Javaheri (2005) and Zhang and Zhu(2006) to estimate implied volatility and conducted the empirical analysis with the historical volatility (HV) and the Volatility index (VIX). The empirical results indicated that volatility index is the best forecast for realized volatility in U.S. market, and historical volatility is the best forecast for realized volatility in Taiwan market. The implied volatility from option market performs better than implied volatility from stock market in forecasting realized volatility in U.S. market. Contrary U.S. market, the implied volatility from stock market has more explanatory power in forecasting realized volatility in Taiwan market. Overall, implied volatility does contain information in forecasting realized volatility in both U.S. and Taiwan market.[[note]]碩