In this article, we present a simulator conceived for the conceptual study of an AO-fed high-contrast coronagraphic imager. The simulator implements physical optics: a complex disturbance (the electric field) is Fresnel-propagated through any user-defined optical train, in an end-to-end fashion. The effect of atmospheric residual aberrations and their evolution with time can be reproduced by introducing in input a temporal sequence of phase screens: synthetic images are then generated by co-adding instantaneous PSFs. This allows studying with high accuracy the impact of AO correction on image quality for different integration times and observing conditions. In addition, by conveniently detailing the optical model, the user can easily implement any coronagraphic set-up and introduce optical aberrations at any position. Furthermore, generating multiple images can allow exploring detection limits after a differential post-processing algorithm is applied (e.g. Angular Differential Imaging). The simulator has been developed in the framework of the design of SHARK-NIR, the second-generation high contrast imager selected for the Large Binocular Telescope.