The importance of being scrambled: supercharged Quasi Monte Carlo

Abstract

In many financial applications Quasi Monte Carlo (QMC) based on Sobol low-discrepancy sequences (LDS) outperforms Monte Carlo showing faster and more stable convergence. However, unlike MC QMC lacks a practical error estimate. Randomized QMC (RQMC) method combines the best of two methods. Application of scrambled LDS allow to compute confidence intervals around the estimated value, providing a practical error bound. Randomization of Sobol' LDS by two methods: Owen's scrambling and digital shift are compared considering computation of Asian options and Greeks using hyperbolic local volatility model. RQMC demonstrated the superior performance over standard QMC showing increased convergence rates and providing practical error bounds.