The nonlinear optical properties of an exciton in a spherical quantum dot (QD) is studied analytically. The nonlinear optical coefficients are calculated within the density matrix formalism. The electronic problem is solved within the effective mass approximation. The contributions from the competing effects of the confinement, the Coulomb interaction, and the applied electric field are calculated and compared with each other. We have made no assumptions about the strength of the confinement. We concentrate the effect of the Coulomb interaction. Our results may provide an input for optimization of the nonlinear optical coefficients. (C) 2015 Elsevier B.V. All rights reserved.