Abstract: In this paper, a two-factor stochastic volatility jump-diffusion model with fluctuating interest rate is presented. Specifically, we define the fluctuating interest rate as a linear combination of two random volatility events with jumps. On the basis of this paradigm, we investigate the pricing complexity of European compound call options. Our contribution is to extract the semi-analytical formulations of these options and calculate the option price using fast Fourier transform (FFT) and Monte Carlo (MC) simulation methods. In addition, we conduct a thorough sensitivity analysis of the selected parameters. Our numerical tests show that our approach has potential advantages when both volatility and jump risk are taken into consideration, particularly when double volatility is considered.