Four-wave mixing is investigated when chirped pump and signal pulses are injected in a photonic crystal fiber. The shot-to-shot stability of the amplified coherent signal was measured by using the dispersive Fourier transform method and compared with numerical simulations. We highlight that the signal-to-noise ratio (SNR) of the pulsed signal increases with the injected power and show that it is not deteriorated through the amplification when the fiber optical parametric amplifier is strongly saturated. The SNR of the signal remains nearly constant after the amplifier.