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

34 Pages Posted: 18 Feb 2016

Date Written: February 18, 2016

Abstract

We investigate further the random generators used in finance Monte Carlo simulation: Mersenne Twister and Sobol Quasi-Random Generator. We focus the analysis on the statistical properties of the random numbers generated across multiple dimensions in Monte Carlo finance simulation. We particularly focus on the distributions and processes used in the estimation of conditional expectation in a finance framework when using Mersenne Twister and Sobol generators.

We characterize the convergence properties of the sample distributions by relying on empirical distribution theory. Then, we provide practical analysis on the convergence of distribution encountered in finance problems. Finally, we characterize the differences of the random generators when simulating such processes.

Keywords: Mersenne Twister, Sobol, Quasi Random, Monte Carlo, Empirical Distribution, C, GPU, Gaussian distribution, Lognormal distribution, Brownian Bridge

JEL Classification: C15

Suggested Citation

Noel, Kevin, Convergence Analysis of Random Generators in Monte Carlo Simulation: Mersenne Twister and Sobol (February 18, 2016). Available at SSRN: https://ssrn.com/abstract=2734013 or http://dx.doi.org/10.2139/ssrn.2734013

Kevin Noel (Contact Author)

ING ( email )

Tokyo
Japan

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