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Application of Quasi Monte Carlo and Global Sensitivity Analysis to Option Pricing and Greeks

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  • Stefano Scoleri
  • Marco Bianchetti
  • Sergei Kucherenko

Abstract

Quasi Monte Carlo (QMC) and Global Sensitivity Analysis (GSA) techniques are applied for pricing and hedging representative financial instruments of increasing complexity. We compare standard Monte Carlo (MC) vs QMC results using Sobol' low discrepancy sequences, different sampling strategies, and various analyses of performance. We find that QMC outperforms MC in most cases, including the highest-dimensional simulations, showing faster and more stable convergence. Regarding greeks computation, we compare standard approaches, based on finite differences (FD) approximations, with adjoint methods (AAD) providing evidences that, when the number of greeks is small, the FD approach combined with QMC can lead to the same accuracy as AAD, thanks to increased convergence rate and stability, thus saving a lot of implementation effort while keeping low computational cost. Using GSA, we are able to fully explain our findings in terms of reduced effective dimension of QMC simulation, allowed in most cases, but not always, by Brownian Bridge discretization or PCA construction. We conclude that, beyond pricing, QMC is a very effcient technique also for computing risk measures, greeks in particular, as it allows to reduce the computational effort of high dimensional Monte Carlo simulations typical of modern risk management.

Suggested Citation

  • Stefano Scoleri & Marco Bianchetti & Sergei Kucherenko, 2026. "Application of Quasi Monte Carlo and Global Sensitivity Analysis to Option Pricing and Greeks," Papers 2602.14354, arXiv.org.
    • Handle: RePEc:arx:papers:2602.14354
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    References listed on IDEAS

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    1. 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.
    2. Luca Capriotti, 2015. "Likelihood Ratio Method and Algorithmic Differentiation: Fast Second Order Greeks," Algorithmic Finance, IOS Press, vol. 4(1-2), pages 81-87.
    3. Mark Broadie & Paul Glasserman, 1996. "Estimating Security Price Derivatives Using Simulation," Management Science, INFORMS, vol. 42(2), pages 269-285, February.
    4. Liu, Ruixue & Owen, Art B., 2006. "Estimating Mean Dimensionality of Analysis of Variance Decompositions," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 712-721, June.
    5. Spassimir H. Paskov & Joseph F. Traub, 1995. "Faster Valuation of Financial Derivatives," Working Papers 95-03-034, Santa Fe Institute.
    6. Damiano Brigo & Fabio Mercurio, 2006. "Interest Rate Models — Theory and Practice," Springer Finance, Springer, edition 0, number 978-3-540-34604-3, December.
    7. Sobol Ilya M. & Shukhman Boris V., 2014. "Quasi-Monte Carlo: A high-dimensional experiment," Monte Carlo Methods and Applications, De Gruyter, vol. 20(3), pages 167-171, September.
    8. A. Papageorgiou & J. F. Traub, 1996. "New Results on Deterministic Pricing of Financial Derivatives," Working Papers 96-06-040, Santa Fe Institute.
    9. Xiaoqun Wang, 2009. "Dimension Reduction Techniques in Quasi-Monte Carlo Methods for Option Pricing," INFORMS Journal on Computing, INFORMS, vol. 21(3), pages 488-504, August.
    10. Luca Capriotti & Mike Giles, 2010. "Fast Correlation Greeks by Adjoint Algorithmic Differentiation," Papers 1004.1855, arXiv.org.
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