A study of the photophysical properties of nitrogen-vacancy (NV) color centers in diamond nanocrystals of size of 50~nm or below is carried out by means of second-order time-intensity photon correlation and cross-correlation measurements as a function of the excitation power for both pure charge states, neutral and negatively charged, as well as for the photochromic state, where the center switches between both states at any power. A dedicated three-level model implying a shelving level is developed to extract the relevant photophysical parameters coupling all three levels. Our analysis confirms the very existence of the shelving level for the neutral NV center. It is found that it plays a negligible role on the photophysics of this center, whereas it is responsible for an increasing photon bunching behavior of the negative NV center with increasing power. From the photophysical parameters, we infer a quantum efficiency for both centers, showing that it remains close to unity for the neutral center over the entire power range, whereas it drops with increasing power from near unity to approximately 0.5 for the negative center. The photophysics of the photochromic center reveals a rich phenomenology that is to a large extent dominated by that of the negative state, in agreement with the excess charge release of the negative center being much slower than the photon emission process.
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