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 languageEnglish
JournalAnnals of Applied Probability
Publication statusAccepted/In press - 7 Apr 2024

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