We propose a new Monte Carlo-based estimator for digital options with assets modelled by a stochastic differential equation (SDE). The new estimator is based on repeated path splitting and relies on the correlation of approximate paths of the underlying SDE that share parts of a Brownian path. Combining this new estimator with Multilevel Monte Carlo (MLMC) leads to an estimator with a complexity that is similar to the complexity of a MLMC estimator when applied to options with Lipschitz payoffs.

翻译：我们提出一个新的以蒙特卡洛为基础的数字选项估算器,其资产以随机差分方程(SDE)为模型。新的估算器基于重复的分解路径,并依赖与布朗路部分部分相共享的基本SDE的近似路径的关联性。 将这一新估算器与多层蒙特卡洛(MLMC)合并,导致一个与MLMC估算器复杂程度相似的估算器,该估算器在应用到与Lipschitz付款的选项时,具有与MLMC估算器的复杂性。