Parametric resonance is a highly nonlinear phenomenon, difficult to model and foresee, with often detrimental consequences on the power production efficiency of wave energy converters. Parametric excitation, due to time-varying parameters of the system, activates an internal excitation mechanism, which diverts part of the energy from the principal degree of freedom, consequently generating parasitic motions. Although the ability of a mathematical model to articulate parametric instability is beneficial for design and control purposes, the increase in computational burden and complexity is often unacceptable. However, using computationally frugal nonlinear Froude-Krylov force calculations, applicable to axisymmetric devices, it is possible to define mathematical models fast enough for computation in real time. The focus of the paper is a floating oscillating water column device, inspired by the Sparbuoy device, in order to demonstrate the ability of such a mathematical model to describe parametric roll responses.