October 2024 Multilevel path branching for digital options
Michael B. Giles, Abdul-Lateef Haji-Ali
Author Affiliations +
Ann. Appl. Probab. 34(5): 4836-4862 (October 2024). DOI: 10.1214/24-AAP2083

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.

Funding Statement

MBG gratefully acknowledges research funding from the UK EPSRC (ICONIC programme Grant EP/P020720/1), and the Hong Kong Innovation and Technology Commission (InnoHK Project CIMDA).

Acknowledgments

We thank Soeren Wolfers for the helpful discussion regarding Lemma 5.2.

Citation

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Michael B. Giles. Abdul-Lateef Haji-Ali. "Multilevel path branching for digital options." Ann. Appl. Probab. 34 (5) 4836 - 4862, October 2024. https://doi.org/10.1214/24-AAP2083

Information

Received: 1 September 2022; Revised: 1 December 2023; Published: October 2024
First available in Project Euclid: 26 September 2024

MathSciNet: MR4801583
zbMATH: 07927503
Digital Object Identifier: 10.1214/24-AAP2083

Subjects:
Primary: 65C05 , 65C30
Secondary: 60J85 , 65B99

Keywords: branching processes , computational complexity , Monte Carlo , multilevel , path splitting

Rights: Copyright © 2024 Institute of Mathematical Statistics

Vol.34 • No. 5 • October 2024
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