Coherent vortices are known to play an important role in transport processes of ideal flows such as two-dimensional and quasi-geostrophic turbulent flows. In this paper, their effect on eddy dispersion and diffusivity is studied in a realistic oceanic flow, using synthetic Lagrangian data simulated within a high-resolution ocean general circulation model in the Gulf Stream recirculation region. The possibility of using a Lagrangian Stochastic Model (LSM) with nonzero mean spin statistic, Ω, to parameterize the observed characteristics is considered. The probability distribution of the Ω parameter (which is representative of the looping behavior of trajectories embedded inside the coherent vortices) is also studied.The main result is that the LSM with a tri-modal Ω-distribution is able to reproduce the eddy diffusivity and dispersion characteristics, especially at short and intermediate time scales. Particularly well predicted are the effects of the coherent vortices, which are the enhanced spreading of particles at short times due to the high eddy energy of the vortices and the inhibited diffusion at intermediate times due to the vortex trapping mechanisms. The LSM parameterization of eddy dispersion is shown to be more appropriate than the commonly used asymptotic eddy-diffusivity approximation. More complex than tri-modal distributions of mean spin are also considered in the LSM, and they are found to produce only slight changes in the predictions of eddy statistics and dispersion.