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
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
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