•This paper develops a general methodology for modeling and pricing financial derivatives which depend on systems of stochastic diffusion processes.•Weak convergence of the approximation is demonstrated, with second order convergence in space.•Numerical experiments demonstrate the accuracy and efficiency of the method for various European and early-exercise options in two and three dimensions Continuous time Markov Chain (CTMC) approximation techniques have received increasing attention in the option pricing literature, due to their ability to solve complex pricing problems, although existing approaches are mostly limited to one or two dimensions. This paper develops a general methodology for modeling and pricing financial derivatives which depend on systems of stochastic diffusion processes. This is accomplished with a general decorrelation procedure, which reduces the system of correlated diffusions to an uncorrelated system. This enables simple and efficient approximation of the driving processes by univariate CTMC approximations. Weak convergence of the approximation is demonstrated, with second order convergence in space. Numerical experiments demonstrate the accuracy and efficiency of the method for various European and early-exercise options in two and three dimensions.