An optimized concept of axisymmetric concentric two-body wave energy converter is proposed, consisting of a torus and a floater, which are outer and inner bodies, respectively. The energy extraction is based on the relative motion of the bodies, which is the heave motion. The hydrodynamic characteristics of the two-body system are analyzed in the frequency-domain to evaluate the efficiency in sub-optimal conditions and an extended coupled hydrodynamic model is developed in the frequency and time-domain. To obtain the hydrodynamic coefficients of the two bodies, an open-source boundary element method code is used. The code is validated with the results of a similar concept. The time-domain model and simulator are developed based on the hydrodynamic coefficients calculated in the frequency-domain. A simplified power take-off system including a realistic hydraulic cylinder is modeled in the time domain and used for the optimization process. The optimization considers the hydrodynamic efficiency of different torus shapes and maximizing the pressure and power in the hydraulic power take-off system. The results show that the cone shape torus presents higher efficiency while the max-mean power ratio of the wave energy converter is compared in different cylinder sizes with optimal power take-off parameters.