Abstract

We combine the Multi-level Monte Carlo (MLMC) method with the numerical scheme for the Heston model that simulates the variance process exactly and applies the stochastic trapezoidal rule to approximate the time integrated variance process in the SDE of the logarithmic asset process. We deal with the simulations for path-independent options and for path-dependent options separately. In both situations, novel MLMC estimators are established and the analytical convergence rates for these estimators are derived for the full parameter regime.

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