Kurtosis in black-scholes model with Garch volatility

The famous Black-Scholes option pricing model is a mathematical description of financial market and derivative investment instruments [3]. In Black-Scholes model volatility is a constant function, where trading option is indeed risky due to random components such as volatility. The notion of non constant volatility was introduced in GARCH processes [6]. Recently a Black-Scholes model with GARCH volatility has been presented [10]. In this article we derive the kurtosis formula for underlying financial time series using BS-Model with GARCH volatility for the case of at the money option. We present the kurtosis formula in terms of the model's parameters. Also we compare our computational results by using another measure of kurtosis for different values of volatilities.