A new 6-DOF nonlinear mathematical model based on Taylor-series expansions with coupling terms defined up to the third-order is introduced and validatedl for head seas parametric rolling for the case of a fishing vessel and a container vessel. Additionally, a large and deep drafted cylindrical SPAR platform is also simulated. The nonlinear algorithm is systematically simulated for different wave conditions. Parametric amplification domains (PADs) are thus obtained for the three hulls. On a comparative basis some of their main characteristics are then examined: influence of coupling, relevance of third-order coupling terms, impact of roll/roll nonlinearities, influence of wave amplitude, and initial conditions. The main differences in the PADs for the three distinct floating vessels are then interpreted and aspects of interest for the modeling and simulation of different hull forms are discussed.