Generating low-discrepancy sequences from the normal distribution: Box-Muller or inverse transform?

Authors:
Giray ÖKten;Ahmet GöNcü
Affiliations:
Department of Mathematics, Florida State University, Tallahassee, FL 32306-4510, USA;The Center for Economic Research, Shandong University, Shanda Nanlu 27, Jinan 250100, China
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2011

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Abstract

Quasi-Monte Carlo simulation is a popular numerical method in applications, in particular, economics and finance. Since the normal distribution occurs frequently in economic and financial modeling, one often needs a method to transform low-discrepancy sequences from the uniform distribution to the normal distribution. Two well known methods used with pseudorandom numbers are the Box-Muller and the inverse transformation methods. Some researchers and financial engineers have claimed that it is incorrect to use the Box-Muller method with low-discrepancy sequences, and instead, the inverse transformation method should be used. In this paper we prove that the Box-Muller method can be used with low-discrepancy sequences, and discuss when its use could actually be advantageous. We also present numerical results that compare Box-Muller and inverse transformation methods.