We provide a highly accurate and fast solver to get an approximate solution of (degenerate) parabolic partial differential equations (PDEs) with variable, but factorising coefficients over a rectangular domain in three space dimensions subject to an arbitrary combination of different boundary conditions. The solver is based on a finite difference discretisation of 4-th order in space and a ADI time marching scheme supplemented with a Richardson extrapolation and is easy to implement. The proposed solver is applied to different derivative pricing problems appearing in continuous time finance such as pricing basket and exotic options in different stochastic volatility models. In particular, we are able to price lookback options in the Double Heston model or European and barrier options in the Heston model with stochastic correlation to high accuracy within a fraction of a second. This extends and unifies recent, tailor made solutions to these pricing problems in the scientific literature.