In this Master’s thesis, we present one of the many applications of the volatility model on derivatives. The focus is on the GARCH model as one of the most significant and frequently used volatility models for financial time series. In the beginning, we present the already known results and tools for time series and their application in finance. We provide insight into volatility models through understanding the basic concept of volatility, the motivation behind studying such models, as well as the application in option pricing. Also, we briefly introduce the ARCH model which is the forerunner of the GARCH model that we observe in more detail. Moreover, we present the theorem that gives the necessary and sufficient conditions under which the GARCH (p, q) model is weakly stationary. Furthermore, we observe some modifications of the model itself and its extensions. The following chapter is the backbone of this paper in which we present the option pricing model where the conditional variance of the log-return of financial assets follows the GARCH (p, q) process. Finally, we conclude the thesis with a practical example illustrated in the programming language R, where we apply the theoretical results to actual data for the european call option pricing and the corresponding delta.