High-order compact finite difference scheme for option pricing in stochastic volatility models

We derive a new compact high-order finite difference scheme for option pricing in stochastic volatility models. The scheme is fourth order accurate in space and second order accurate in time. To prove results on the unconditional stability in the sense of von Neumann we perform a thorough Fourier analysis of the problem and deduce convergence of our scheme. We present results of numerical experiments for the European and American option pricing problem.