The pricing of options in the fast mean-reverting stochastic volatility model using the singular perturbation method has received a considerable amount of attention in the last two decades. However, it is not to easy to estimate the accuracy of the approximation if the payoff function is not smooth or bounded, as is the case for European call options. In this article, we introduce a new novel approach for pricing options in the fast mean-reverting stochastic volatility model. Combinations of Fourier analysis and singular perturbation methods enable us to estimate the accuracy easily. We also show that this method allows us to derive the price of European and Bermudan options in the fast mean-reverting stochastic volatility environment with jumps. (C) 2017 Elsevier B.V. All rights reserved.