Low-Discrepancy Sequences

Abstract

is an associate professor at San Francisco State University's College of Business.This article examines the use of Monte Carlo simulation with low-discrepancy sequences (or quasi-Monte Carlo) for valuing complex derivatives contracts versus the more traditional Monte Carlo method using random sequences. Unlike the latter, low-discrepancy (or quasi-random) sequences are deterministic.Some research has hinted that low-discrepancy sequences improve the rate of convergence of Monte For a large sample of simulated price paths, the mean of the sample will closely approximate the derivative's true price [i.e., Equation (1)]. The rate of convergence is (J/ -iN, where (J is the standard deviation of the population, and N is the number of simulations (price paths).Unfortunately, the rate of convergence is 64

Determining predictive uncertainties and global sensitivities for large parameter systems: A case study for n -butane oxidation

“…Subsequently model A normal distribution of random numbers can be obtained from a uniform distribution of random numbers using the Box-Muller algorithm (e.g., [22]). However, for low discrepancy sequences, it should be avoided because it may damage their intrinsic properties, either by altering the order of the sequence or by scrambling the sequence uniformity [23,24]. We therefore compute directly the inverse normal distribution of the Sobol sequence given its cumulative distribution function 2 .…”

A new look at the topographical global optimization method and its application to the phase stability analysis of mixtures

“…In this work, we employ the so-called Sobol sequence (Sobol, 1967), which is a deterministic sequence with low discrepancy, see, for example, Gentle (2003) and Galanti and Jung (1997).…”

A Toolbox for Quasirandom Simulation

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