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.

中文翻译：

---

Heston 随机波动率模型的多级蒙特卡罗模拟

我们将多级蒙特卡罗 (MLMC) 方法与 Heston 模型的数值方案相结合，精确或几乎精确地模拟方差过程，并应用随机梯形规则来近似对数资产过程的 SDE 内的时间积分方差过程。我们对路径无关选项和路径相关选项进行单独的模拟。在这两种情况下，都建立了新颖的 MLMC 估计器，并导出了全参数体系的理论收敛率。我们提供数值结果来证明我们的 MLMC 估计器的效率。