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Multilevel Path Branching for Digital Options

Numerical Analysis 2024-06-19 v2 Numerical Analysis Computational Finance

Abstract

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 This preprint includes detailed calculations and proofs (in grey colour) which are not peer-reviewed and not included in the published article.

Keywords

Cite

@article{arxiv.2209.03017,
  title  = {Multilevel Path Branching for Digital Options},
  author = {Michael B. Giles and Abdul-Lateef Haji-Ali},
  journal= {arXiv preprint arXiv:2209.03017},
  year   = {2024}
}
R2 v1 2026-06-28T00:51:49.114Z