Optical Fabry–Perot cavity with a movable mirror is a paradigmatic optomechanical system. While usually the mirror is supported by a mechanical spring, it has been shown that it is possible to keep one of the mirrors in a stable equilibrium purely by optical levitation without any mechanical support. In this work, we expand previous studies of the nonlinear dynamics of such a system by demonstrating a possibility for mechanical parametric instability and the emergence of the “phonon laser” phenomenon.