Abstarct: This thesis is baxsed on the FFT (Fast Fourier Transform) approach for the valuation of options when the underlying asset follows the double exponential jump process with stochastic volatility and stochastic intensity. Our model captures three terms structure of stock prices the market implied volatility smile, and jump behavior. Via the FFT method, numerical examples using European call options show effectiveness of the proposed model. Meanwhile numerical results prove that the FFT approach is considerably correct, fast and competent.