An all-fiber optical parametric oscillator comprising a highly nonlinear optical fiber and wavelength division multiplexing couplers is numerically simulated. The model is based on a set of coupled nonlinear Schrödinger equations which spectrally resolve the gain bandwidth of the pump, signal and idler waves. We show that such high wavelength resolution is necessary to obtain the correct threshold pump powers, stationary output powers, and relative intensity noise. Finally, we compare seeded and unseeded configurations and find that the seeded configuration generates low-noise idler output at conversion efficiencies of up to 10% below the threshold power for unseeded operation, but that both seeded and unseeded oscillators produce comparable results above threshold.