In this thesis I study the optical properties of a hybrid nanoparticle consisting of a metal and a semiconductor part. I examine the electrostatic influence of the metallic particle on the exciton states. Further, I calculate the effect of the semiconductor on the plasmon that is optically created on the metal surface. I derive a framework to calculate the polarization of the semiconductor due to the external and plasmonic fields, and use it to obtain the scattering and absorption spectra for the combined particle.I treat a model system where the semiconductor is approximated by a few material specific parameters and the geometry is a match stick shaped structure with a semiconducting rod and a metallic tip. For our simulations I use the MNPBEM toolbox for Matlab, which uses the boundary element method for the calculation of electromagnetic potentials. I find that the optical response of the combined particle is enhanced with respect to the response of separated particles. Exciton resonances are shifted to lower energies in the presence of a metal and the exciton-dipole self interaction via the environment appears to have very little effect on the optical properties.