Application of Quasi Monte Carlo and Global Sensitivity Analysis to Option Pricing and Greeks: Finite Differences vs. AAD

Quasi Monte Carlo (QMC) and Global Sensitivity Analysis (GSA) techniques are applied to pricing and hedging of representative financial instruments with 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 difference (FD) approximations, with Adjoint Algorithmic Differentiation (AAD) methods providing evidence that, when the number of greeks is small, switching from MC to QMC simulation, the FD approach 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 by Brownian bridge discretization or Principal Component Analysis (PCA) construction. We conclude that, beyond pricing, QMC is a very efficient technique also for computing risk measures, greeks in particular, as it allows us to reduce the computational effort of high-dimensional Monte Carlo simulations typical of modern risk management.