Generating low-discrepancy sequences from the normal distribution: Box–Muller or inverse transform?
✍ Scribed by Giray Ökten; Ahmet Göncü
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 744 KB
- Volume
- 53
- Category
- Article
- ISSN
- 0895-7177
No coin nor oath required. For personal study only.
✦ Synopsis
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.