Effective dimensionality reduction for Greeks computation using Randomized QMC

ArXiv ID: 2504.11576 “View on arXiv”

Authors: Unknown

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.

Keywords: global sensitivity analysis, Chebyshev interpolation, pathwise method, randomized Quasi Monte Carlo, importance sampling, Derivatives (Barrier options, Asian options)

Complexity vs Empirical Score

• Math Complexity: 9.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematical techniques including randomized QMC, global sensitivity analysis (Sobol’ indices), and Chebyshev interpolation for Greeks computation, requiring dense theoretical derivations. It demonstrates strong empirical rigor by backtesting on specific exotic options (Asian and barrier options) with comparative numerical results against standard Monte Carlo and finite difference methods, though it lacks the breadth of live trading data.

  flowchart TD
    A["Research Goal<br>Improve Greeks Computation<br>Reduce Effective Dimensionality"] --> B["Methodology"]
    B --> C["Data & Inputs<br>Discretely Monitored Barrier Options<br>Arithmetic Average Asian Options"]
    C --> D["Computational Processes<br>Global Sensitivity Analysis<br>Compare MC/FD, RQMC/BB, Chebyshev/Pathwise<br>Test Importance Sampling"]
    D --> E["Key Findings & Outcomes<br>Chebyshev/Pathwise increase smoothness<br>Reduced Effective Dimensionality<br>RQMC convergence rate improves<br>Higher accuracy & Lower cost"]