Multilevel Monte Carlo simulation for the Heston stochastic volatility model

We combine the multilevel Monte Carlo (MLMC) method with a numerical scheme for the Heston model that simulates the variance process exactly or almost exactly and applies the stochastic trapezoidal rule to approximate the time-integrated variance process within the SDE of the logarithmic asset process. We conduct separate simulations for path-independent options and path-dependent options. In both situations, novel MLMC estimators are established, and the theoretical convergence rates are derived for the full parameter regime. We present numerical results to demonstrate the efficiency of our MLMC estimators.