A hybrid approach for the implementation of the Heston model

We propose an efficient hybrid tree/finite difference method in order to approximate the Heston model (and possibly other stochastic volatility models). We prove the convergence by embedding the procedure in a bivariate Markov chain and we study the approximation of European and American option prices. We finally provide numerical experiments that give accurate option prices in the Heston model, showing the reliability and the efficiency of the algorithm.