In this talk, we consider the efficient simulation of asset prices for general stochastic local volatility models, which include the Heston stochastic volatility model and the stochastic alpha beta rho (SABR) model as special cases. Our simulation algorithm is constructed based on a novel application of a continuous-time Markov chain (CTMC) approximation to the latent stochastic variance process. Compared with traditional time discretization approaches, our method exhibits several advantages, including a second order convergence rate in the space of the approximating CTMC under suitable regularity conditions. Replacing the stochastic variance process with a discrete-state approximation greatly simplifyies the direct sampling of the integrated variance, thus enabling a highly efficient semi-exact simulation scheme. Extensive numerical examples illustrate the efficiency of our estimator, which compares favorably to existing biased or unbiased simulation estimators in the literature. This new approach to simulation has the potential for numerous applications which involve the estimation of path-dependent functionals of a diffusion process. (Joint with Zhenyu Cui and J. Lars Kirkby)