This can probably be achieved with time dependent density functional theory, however it's nontrivial. Regrettably, I have no real experience in this area, however TD-DFT is a good place to start if you're interested in calculating UV/Vis and (hyper)polarisability properties almost from first principles.
Good electronic structure codes should be capable of directly outputting UV/Vis spectra, whilst the refractive index is related to the unit cell of the material and the frequency dependent polarisability tensor(1). Accordingly, you'll only be able to get hard results for crystalline glycerol, rather than liquid or glassy phases, however the index may not change much. Because the index is frequency dependent, you may have to do calculations over a subdivided range of frequencies, which may be quite time consuming.
You might want to look at software packages such as GAUSSIAN, ADF, GAMESS/Firefly, ORCA, MPQC, NWChem, etc., which range in price between free and very expensive.
Alternatively, if you have access to the right facilities, you could always make empirical measurements in about 5 minutes, but where's the fun in that?
edit: regarding Georg's statement answer, glycerol has a small absorption in the range of interest.
(1) Tossell, J. A. and Lazzeretti, Paolo; Ab initio calculation of the refractive indices and related properties of $CaCO_{3}$; Phys. Rev. B; 38, 8, 1988, pp. 5694-5698