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Volalitity is not only the key factor to determine the price of assets but also the risky index of underlying assets. There are many volatility farecasting models and none of them are perfect. To compare the performance of these model, this study uses 2007 to 2009 TAIEX futures data to construct three volatility forecast models, which are historical volatility, time series volatility, and implid volatility model. Base on the MAE, RMSE and MAPE criterions. we find that VIX combine GJR-GARCH model performs well in forcasting volatility. This implies the leverage effect do exist in the Taiwan stock market and futures market.
This study also tries to find the gap between GJR-GARCH Model and impled volatility. First the GJR-GARCH volatility and implied volatility almost move together in most of the days. However, when the day near the delivery date of options, the impled volatility jump up suddenly and the closer to the delivery date, the larger gap between these two volatilities. The intuition behind this is due to the worry of a suddenly shock before delivery date will encourge options writers to ask for higher premium to compensate the risk of volatility shock. Furthermore, the implied volatility of put is always greater than that of call options. This implied that the investors are more afraid of down side risk than up side risk. Knowning this fact, this study constructs a volatility forecasting model by adding dummy variables to count the near-delivery-date effect. This model outperforms other volatility models in forecasting the options prices.
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