| Summary: | 碩士 === 國立臺灣大學 === 商學研究所 === 91 === Abstract
Forecasting the volatility of underlying asset has always been a major concern of option pricing and hedging. Many volatility forecasting models have been developed after dozens of researches and studies. Except for econometrics and quantitative models, using option implied volatility as the estimator of future volatility has also been extensively accepted by the academia and market. The major drawback of ISD is that it will differ from option exercise price and maturity, which is known as the volatility-skew. In 1993, the CBOE introduced the Market Volatility Index（VIX） based on S&P100 index options implied volatilities. The VIX provides a standard, reliable and real-time estimate of short-term market volatility to the market participants. Because of the success of the VIX, the CBOE continued to introduce the volatility index based on Nasdaq100 index options（VXN）. Other countries, such as French, Germany and Swiss, have developed the volatility index for their own markets based option implied volatilities as well.
This article could be divided into three parts. First, we compare the characteristics and construction methods of the volatility indices across different countries. Second, we use the data of TAIEX index options（TXO）to construct the volatility index for TAIEX（TVX）and test the forecasting power of TVX with historical estimation method. Besides, we have also examined the relationship between the TVX and TAIEX. Finally, we illustrate some applications of the volatility index. The conclusions are as follows：
1. In our sample period, using delta to decide ATM options with both call and put options to calculate TVX provides the best forecasting performance. Furthermore, the TVX outperforms the volatility estimation method which using historical data.
2. The TVX has negative and asymmetry relationship with the TAIEX simultaneously. The TVX is more sensitive to the decrease of the TAIEX than the increase, which is agree with previous studies.
3. Based on daily trading data, the TVX seems to lead the TAIEX for 3 days. But this inference is not very significant.
4. There isn’t an obvious intraweek effect of TVX. Besides, the expiration of TXO doesn’t influence the TVX.
5. According to our examination, the TVX could be a useful trading signal for the TAIEX. When the TVX reaches its relative height, one can reap positive returns by buying the TAIEX. Moreover, derivatives of the volatility index could be an effect tool for vega hedging.
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