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

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 difference 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 us to reduce the computational effort of high-dimensional MC simulations typical of modern risk management.