We report a multiscale modeling approach to study static and dynamical properties of polymer melts at large time and length scales. We use a bottom-up approach consisting of deriving coarse-grained models from an atomistic description of the polymer melt. We use the iterative Boltzmann inversion (IBI) procedure and a pressure-correction function to map the thermodynamic conditions of the atomistic configurations. The coarse-grained models are incorporated in the dissipative particle dynamics (DPD) method. The thermodynamic, structural, and dynamical properties of the cis-1,4-polybutadiene melt are very well reproduced by the coarse-grained DPD models with a significative computational gain. We complete this study by addressing the challenging question of the investigation of the shear modulus evolution. As expected from experiments, the stress correlation functions show behaviors that are dependent on the molecular weights defining unentangled and weakly entangled polymer melts.