Accurate and computationally efficient mathematical models are fundamental for designing, optimizing, and controlling wave energy converters. Many wave energy devices exhibit significant nonlinear behaviour over their full operational envelope, so nonlinear models may become indispensable. Froude-Krylov nonlinearities are of great importance in point absorbers but, in general, their calculation requires an often unacceptable increase in model complexity/computational time. However, for axisymmetric bodies, it is possible to describe the whole geometry analytically, thereby allowing faster calculation of nonlinear Froude-Krylov forces. In this paper, a convenient parametrization of axisymmetric body geometries is proposed, applicable to devices moving in surge, heave, and pitch. While, in general, Froude-Krylov integrals must be solved numerically, by assuming small pitch angles, it is possible to simplify the problem, and achieve a considerably faster algebraic solution. However, both nonlinear models compute in real-time. The framework presented in the paper offers flexibility in terms of computational and fidelity levels, while still representing important nonlinear phenomena such as parametric pitch instability. Models with lower computational requirements may be more suitable for repetitive calculations, such as real-time control, or long-term power production assessment, while higher fidelity models may be more appropriate for maximum load estimation, or short-term power production capability assessment.