Paper: arXiv 2602.14354

Authors: 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.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 7.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a rigorous empirical evaluation of Quasi Monte Carlo (QMC) and Global Sensitivity Analysis (GSA) applied to derivative pricing and Greeks calculation. It offers strong mathematical foundations linking low-discrepancy sequences, ANOVA, and effective dimensions to numerical performance, backed by comprehensive speed-up and stability analyses.

Research Flowchart

  flowchart TD
    A["Research Goal:<br>Evaluate QMC & GSA for Option Pricing<br>and Greeks Computation"] --> B["Financial Inputs:<br>Representative Instruments &<br>Sobol Low Discrepancy Sequences"]
    B --> C["Pricing & Greeks Engine:<br>MC vs. QMC (Sobol) &<br>FD vs. AAD Approaches"]
    C --> D["Dimensionality Analysis (GSA):<br>Assess Effective Dimension via<br>Brownian Bridge & PCA"]
    D --> E["Key Outcomes:<br>1. QMC outperforms MC with faster convergence<br>2. QMC + FD matches AAD accuracy for few Greeks<br>3. GSA explains performance via reduced dimension"]