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 computational complexity that is similar to the complexity of a MLMC estimator when applied to options with Lipschitz payoffs. This preprint includes detailed calculations and proofs (in grey colour) which are not peer-reviewed and not included in the published article.

翻译：本文针对由随机微分方程建模的资产数字期权，提出了一种新的基于蒙特卡洛方法的估计器。该新型估计器基于重复路径分裂，并依赖于共享部分布朗路径的基础随机微分方程近似路径之间的相关性。将此新估计器与多级蒙特卡洛方法相结合，所得估计器的计算复杂度与将多级蒙特卡洛方法应用于具有利普希茨连续收益的期权时的复杂度相当。本预印本包含详细的演算与证明（以灰色标注），这些内容未经同行评审，也未包含在已发表的文章中。