Wave energy devices are designed, and controlled, to be extremely responsive to incoming wave excitation, hence, maximising power absorption. Due to the consequent large motion excursions, highly nonlinear behaviour is likely to occur, especially in relation to variations in wetted surface. Moreover, nonlinearities may induce parametric instability, or activate internal mechanisms for exchanging energy between different degrees of freedom (DoFs), usually affecting the overall efficiency of the device. Consequently, single-DoF linear models may produce overly optimistic power production predictions, and neglect important dynamics of the system. One highly nonlinear phenomenon, potentially detrimental to power absorption for several wave energy converters, is parametric roll/pitch; due to parametric excitation, part of the energy flow is internally diverted, from the axis where the power take-off is installed, to a secondary axis, generating parasitic motion. This paper proposes a computationally efficient multi-DoF nonlinear model, which can effectively describe nonlinear behaviour, such as parametric pitch and roll, and their impact on motion prediction, power production assessment, and optimal control parameters.