Pricing and Risk Management with High-Dimensional Quasi Monte Carlo and Global Sensitivity Analysis

TL;DR

This paper demonstrates that Quasi Monte Carlo methods, combined with Global Sensitivity Analysis, significantly improve the efficiency and stability of high-dimensional financial simulations for pricing and risk management compared to standard Monte Carlo techniques.

Contribution

It provides a comprehensive comparison of QMC and MC in high-dimensional settings and introduces GSA as a tool to explain and optimize QMC performance in financial applications.

Findings

QMC outperforms MC in high-dimensional simulations and greeks calculations.

QMC achieves faster convergence and greater stability than MC.

GSA explains the reduced effective dimension in QMC performance.

Abstract

We review and apply Quasi Monte Carlo (QMC) and Global Sensitivity Analysis (GSA) techniques to pricing and risk management (greeks) of representative financial instruments of increasing complexity. We compare QMC vs standard Monte Carlo (MC) results in great detail, using high-dimensional Sobol' low discrepancy sequences, different discretization methods, and specific analyses of convergence, performance, speed up, stability, and error optimization for finite differences greeks. We find that our QMC outperforms MC in most cases, including the highest-dimensional simulations and greeks calculations, showing faster and more stable convergence to exact or almost exact results. Using GSA, we are able to fully explain our findings in terms of reduced effective dimension of our QMC simulation, allowed in most cases, but not always, by Brownian bridge discretization. We conclude that, beyond pricing, QMC is a very promising technique also for computing risk figures, greeks in particular, as it allows to reduce the computational effort of high-dimensional Monte Carlo simulations typical of modern risk management.