We report experimental and theoretical investigations of ultrafast coherent dynamics in a photonic-crystal point-defect nanocavity. The experimental investigations are carried out using a versatile heterodyne pump-probe setup giving access to wavelength and time-resolved dynamics. We find that parametric processes originating from coherent interactions between the pump and the probe lead to characteristic and clearly distinguishable features in the time-resolved dynamics. The parametric process is caused by fast oscillations of spatially trapped carriers, with the nanocavity acting to enhance the optical fields and thereby the strength of these processes. This interpretation is confirmed by the good agreement that is obtained with a theoretical model, which extends previous works by taking into account wave-mixing effects among the probe and pump pulse. The physics behind the parametric process is explained in detail and a simple expression is derived for the conditions under which coherent interactions lead to high-transmission bands for the probe pulses. These results are important for understanding how coherent effects can be used to improve the dynamical properties of nanocavity switches.