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

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