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Effective dimensionality reduction for Greeks computation using Randomized QMC

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Listed:
  • Luca Albieri
  • Sergei Kucherenko
  • Stefano Scoleri
  • Marco Bianchetti

Abstract

Global sensitivity analysis is employed to evaluate the effective dimension reduction achieved through Chebyshev interpolation and the conditional pathwise method for Greek estimation of discretely monitored barrier options and arithmetic average Asian options. We compare results from finite difference and Monte Carlo methods with those obtained by using randomized Quasi Monte Carlo combined with Brownian bridge discretization. Additionally, we investigate the benefits of incorporating importance sampling with either the finite difference or Chebyshev interpolation methods. Our findings demonstrate that the reduced effective dimensionality identified through global sensitivity analysis explains the performance advantages of one approach over another. Specifically, the increased smoothness provided by Chebyshev or conditional pathwise methods enhances the convergence rate of randomized Quasi Monte Carlo integration, leading to the significant increase of accuracy and reduced computational costs.

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  • Luca Albieri & Sergei Kucherenko & Stefano Scoleri & Marco Bianchetti, 2025. "Effective dimensionality reduction for Greeks computation using Randomized QMC," Papers 2504.11576, arXiv.org.
    • Handle: RePEc:arx:papers:2504.11576
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    References listed on IDEAS

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    1. Chaojun Zhang & Xiaoqun Wang, 2020. "Quasi-Monte Carlo-based conditional pathwise method for option Greeks," Quantitative Finance, Taylor & Francis Journals, vol. 20(1), pages 49-67, January.
    2. Andrea Maran & Andrea Pallavicini & Stefano Scoleri, 2021. "Chebyshev Greeks: Smoothing Gamma without Bias," Papers 2106.12431, arXiv.org.
    3. Marco Bianchetti & Sergei Kucherenko & Stefano Scoleri, 2015. "Pricing and Risk Management with High-Dimensional Quasi Monte Carlo and Global Sensitivity Analysis," Papers 1504.02896, arXiv.org.
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