Pricing financial derivatives such as options with desired accuracy can be hard due to the nature of the functions and complicated integrals required by the pricing techniques. In this paper we investigate the pricing methodology of the European style options using two advanced numerical methods, namely, Quasi-Monte Carlo and Fourier Cosine (COS). For the RQMC method, we use the random-start Halton sequence. We use the Black-Scholes-Merton model to measure the pricing quality of both of the methods. For the numerical results we compute the option price of the call option and we found a few reasons to prefer the RQMC method over the COS method to approximate the European style options.