An Application of Closed-Form GARCH Option Pricing Model to TAIEX Options and Volatilities

Many empirical studies have indicated that the assumption of Black-Scholes model exhibits systematic biases. In practice, Black-Scholes implied volatilities tend to differ across exercise prices and time to maturity. To overcome the shortcoming, many researchers have contributed to substantial new models. In this article, we test the empirical implications based on Heston and Nandi (2000) GARCH model in the TAIEX options market. As a benchmark model we choose the ad hoc BS model that has the flexibility of fitting to the strike and term structure of observed implied volatilities by using a separate implied volatility for each option. It is found that the GARCH model has smaller valuation errors (out-of-sample) than the ad hoc BS model.