The importance of being scrambled: supercharged Quasi Monte Carlo

TL;DR

This paper demonstrates that scrambled Sobol low-discrepancy sequences in randomized Quasi Monte Carlo significantly improve convergence rates and enable practical error estimation in financial computations like Asian options and Greeks.

Contribution

It compares Owen's scrambling and digital shift methods, showing that scrambled LDS enhances RQMC performance over standard QMC in financial applications.

Findings

Scrambled LDS improves convergence rates in RQMC.

Scrambled RQMC provides practical error bounds.

Superior performance of RQMC over standard QMC in financial models.

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.