A concept to flexibly adjust the spectral bandwidth of the output pulses of a fiber optical parametric oscillator is presented. By adjusting the chirp of the pump pulses appropriate to the chirp of the resonant pulses, the energy of the output pulses can be transferred into a user-defined spectral bandwidth. For this concept of optical parametric chirped pulse oscillation, we present numerical simulations of a parametric oscillator, which is able to convert pump pulses with a spectral bandwidth of 3.3 nm into output pulses with an adjustable spectral bandwidth between 9 and 0.05 nm. Combined with a wavelength tunability between 1200 and 1300 nm and pulse energies of up to 100 nJ, the concept should allow to adapt a single all-fiber parametric oscillator to a variety of applications, e.g., in multimodal nonlinear microscopy.