HARMONI, an adaptive optics (AO) assisted integral field spectrograph (IFS), will be the core spectroscopic capability for the European Southern Observatory's (ESO's) Extremely Large Telescope (ELT). It will support several AO modes and achieve diffraction-limited (≈10 mas) to seeing-limited spatial resolution, at low to high spectral resolving powers (λ/∆λ = 3,000-18,000) spanning the visible to near-infrared wavelength range (0.46-2.45 μm). In this paper we describe the modelling of the entire optical science path, from the creation of the end-to-end optical model, over how we analyse the optical performance, to the preliminary results of both nominal and as-built Monte-Carlo instances of HARMONI.