Analysis of Random Generators in Monte Carlo Simulation: Mersenne Twister and Sobol

Abstract

We investigate the random generators used in Finance: Mersenne Twister and Sobol Quasi Random Generator. We focus the analysis on the statistical properties of the random numbers generated at high dimension and over a wide range of dimensions (From 1 to 20000). We describe the degenerate patterns of random numbers produced by Sobol Generator and Randomized Sobol Generator across a wide series of dimension (800 dimension pairs), leading to charaterize those patterns. We provide an algorithm to filter Sobol sequences. Additionally, we mention the used cases in Finance, especially, we highlight the dimensions typically encountered in quantative finance model simulations. We highlight the simulation with CPU/GPU (Graphic Processor Unit) for random numbers generation and leading some conclusions on their practical usage.

Keywords: Monte Carlo in Finance, Sobol generator, Randomized Sobol generator, Mersenne Twister, Pseudo Monte Carlo, Quasi Monte Carlo, statistical analysis, C, GPU programmning, CUDA