| Summary: | 碩士 === 國立中正大學 === 財務金融所 === 97 === Nikki 225 index option was traded in Japan since 1989 and is currently one of the most actively traded derivatives in the market. Nikki 225 starts trading in Taiwan on May 2006, and enjoys high liquidity and zero transaction taxes. When calculating index option prices, all the necessary parameters can be directly observed through the market except for volatility. If one can forecast future volatility correctly, he could therefore obtain the correct option price, greatly facilitate hedging operation.
During bull and bear markets, investors can react quite differently when trading options. Therefore, this paper examines the empirical implication to the pricing of Nikki 225 index option by differentiating between bull market and bear market. Specifically, we employ six volatility models and classify them into time series and non time series group. Time series group includes historical volatility, GARCH (1, 1) model, EGARCH (1, 1) model and GJR-GARCH (1, 1) model. Non time series group includes VXO and VIX. We examine models in the two groups by mean absolute error (MAE), root mean squared error (RMSE), mean absolute percentage error (MAPE) and paired sample T-test. To identify which model is the best one to forecast volatility in five days, ten days and twenty days. Integrating the best volatility in time series group into the best volatility in non time series group to examine whether promote forecasting power or not.
Our findings show that during bull market, historical volatility and EGARCH (1, 1) model have the best forecasting power for five days and ten days. EGARCH (1, 1) model has the best forecasting power for twenty days. On the other hnad, during bear market, EGARCH (1, 1) model exhibit the best forecasting power for all five- ten- and twenty day periods examined.
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