Abstract

This paper aims to propose four volatility measures: The first is the GARCH model advocated by Bollerslev (1986); the second is the GARCH_VIX model which extends the GARCH model by including the volatility index (VIX) as explanatory variable for volatility; the last two are HS_20D and HS_252D, which represent the historical volatilities generated by traditional rolling window technique with 20- and 252-day historical index returns data, respectively. We examine the price information on VIX to improve the predictive performance of GARCH model for valuing TAIEX stock index call options (TXO) over the period from January 2014 to May 2015. Empirical results firstly indicate that both the GARCH and GARCH_VIX models consistently perform better than the historical volatility models for forecasting call value of TXO under different moneynesses. Secondly, the GARCH_VIX model significantly outperforms the GARCH model for most cases, indicating that the GARCH-based option price forecasts can be effectively improved with the additional information contained in VIX. Finally, the use of GARCH_VIX model can greatly reduce model mispricing especially for out-the-money TXO option case. Thus, volatility index is crucial for option traders to efficiently predict TXO option value with GARCH model.

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