  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which are not peer-reviewed and not included in the published article.
