Point absorber wave energy converter (WEC) control strategies often require accurate models for maximum energy extraction. While linear models are suitable for small motions, the focus is on the nonlinear model of an hour-glass shaped buoy undergoing large vertical displacements. Closed-form expressions for the static and dynamic Froude–Krylov forces are developed. It is shown that, in general, the dynamic and static forces are of similar magnitude, which is not the case for a spherical buoy. While the dynamic force reduces the amplitude of the net buoy force, its shape predicts a larger buoy response than if neglected, causing the nonlinear terms to have an even more significant effect. An input-state feedback linearizing controller is developed to show how the nonlinear model can be used in a control law. A 2.5 m buoy example is simulated to illustrate the approach of tracking an arbitrary displacement reference. For the case considered, the extracted power is 30% larger when the nonlinear dynamic FK force is used in the control law. The hourglass buoy is also compared to a spherical buoy to illustrate differences in their response to regular waves and energy extraction when using the same control laws. A spherical buoy diameter of 7.5 m was required to obtain the same power output as a 5 m tall hourglass buoy. A power-force-amplitude (PFA) metric is introduced to compare energy extraction performance and power take-off requirements. The hourglass buoy’s PFA was 13% larger than the spherical buoy implying that it can produce similar power but with less control effort.