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Multilevel Path Branching for Digital Options

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  • Michael B. Giles
  • Abdul-Lateef Haji-Ali

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 This preprint includes detailed calculations and proofs (in grey colour) which are not peer-reviewed and not included in the published article.

Suggested Citation

  • Michael B. Giles & Abdul-Lateef Haji-Ali, 2022. "Multilevel Path Branching for Digital Options," Papers 2209.03017, arXiv.org, revised Jun 2024.
    • Handle: RePEc:arx:papers:2209.03017
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    References listed on IDEAS

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    1. Michael Giles & Desmond Higham & Xuerong Mao, 2009. "Analysing multi-level Monte Carlo for options with non-globally Lipschitz payoff," Finance and Stochastics, Springer, vol. 13(3), pages 403-413, September.
    2. Michael B. Giles, 2008. "Multilevel Monte Carlo Path Simulation," Operations Research, INFORMS, vol. 56(3), pages 607-617, June.
    3. Michael B. Giles & Lukasz Szpruch, 2012. "Antithetic multilevel Monte Carlo estimation for multi-dimensional SDEs without L\'{e}vy area simulation," Papers 1202.6283, arXiv.org, revised May 2014.
    4. Michael B. Giles & Kristian Debrabant & Andreas Ro{ss}ler, 2013. "Analysis of multilevel Monte Carlo path simulation using the Milstein discretisation," Papers 1302.4676, arXiv.org, revised Jun 2019.
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    Cited by:

    1. Abdul-Lateef Haji-Ali & Jonathan Spence, 2023. "Nested Multilevel Monte Carlo with Biased and Antithetic Sampling," Papers 2308.07835, arXiv.org.

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