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

Multilevel Path Branching for Digital Options