Multilevel Path Branching for Digital Options

Michael B. Giles; Abdul-Lateef Haji-Ali

doi:10.1214/24-aap2083

Multilevel Path Branching for Digital Options

Michael B. Giles, Abdul-Lateef Haji-Ali

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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.

Original language	English
Pages (from-to)	4836-4862
Number of pages	27
Journal	Annals of Applied Probability
Volume	34
Issue number	5
Early online date	26 Sept 2024
DOIs	https://doi.org/10.1214/24-aap2083
Publication status	Published - Oct 2024

Keywords

Monte Carlo
branching processes
computational complexity
multilevel
path splitting

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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Multilevel Path Branching for Digital Options

Abstract

Keywords

ASJC Scopus subject areas

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