Predicted results of the structural, electronic and optical properties of the cubic zinc-blende phase of BN, BAs and BP binary compounds and their related ternary and quaternary alloys are presented. The density functional theory (DFT) within full potential linearized augmented plan wave (FP-LAPW) is employed. Different exchange correlation approximations were used to calculate the structural properties as well as the total energies, lattice parameters, bulk modulus and its first pressure derivative. The electronic band structures were treated with the local density approach and Tran Blaha modified Beck-Johnson (TB-mBJ) approximation. A quadratic fit of the lattice parameter, bulk modulus and band gap was performed, where a nonlinear variation with the composition x and y is found. Moreover, the optical properties have been investigated, where the dielectric behavior, the refractive index variations and the loss energy were studied. Furthermore, the electronic and optical properties were computed under hydrostatic pressure. Our results showed great agreement with the previous available experimental and theoretical data found in the literature.