In the present study, the electronic and optical properties of the exciton (X), the biexciton (XX) and charged excitons (X- and X+) in a multi-shell quantum dot nanocrystal have been systematically explored in detail. The electronic properties have been determined in the framework of the single-band effective mass approximation. For this purpose, the Poisson-Schrodinger equations have been solved self-consistently in the Hartree approximation. In the electronic structure calculations for XX, X- and X+, the quantum mechanical exchange-correlation potentials between particles of the same type have been taken into account in the local density approximation. Some optical parameters, such as the overlap integrals, recombination oscillator strengths, radiative lifetimes, etc, have been determined by using the single-particle energy levels and wavefunctions obtained. A different approximation, reported in Sahin and Koc 2013 Appl. Phys. Lett. 102 183103, has been used in the recombination oscillator strength calculations. The results have been presented comparatively as a function of the shell thicknesses, and the well widths and probable physical reasons underlying them have been discussed in detail.