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The acceptance-rejection method for low-discrepancy sequences

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  • Nguyet Nguyen
  • Giray Okten

Abstract

Generation of pseudorandom numbers from different probability distributions has been studied extensively in the Monte Carlo simulation literature. Two standard generation techniques are the acceptance-rejection and inverse transformation methods. An alternative approach to Monte Carlo simulation is the quasi-Monte Carlo method, which uses low-discrepancy sequences, instead of pseudorandom numbers, in simulation. Low-discrepancy sequences from different distributions can be obtained by the inverse transformation method, just like for pseudorandom numbers. In this paper, we will present an acceptance-rejection algorithm for low-discrepancy sequences. We will prove a convergence result, and present error bounds. We will then use this acceptance-rejection algorithm to develop quasi-Monte Carlo versions of some well known algorithms to generate beta and gamma distributions, and investigate the efficiency of these algorithms numerically. We will also consider the simulation of the variance gamma model, a model used in computational finance, where the generation of these probability distributions are needed. Our results show that the acceptance-rejection technique can result in significant improvements in computing time over the inverse transformation method in the context of low-discrepancy sequences.

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  • Nguyet Nguyen & Giray Okten, 2014. "The acceptance-rejection method for low-discrepancy sequences," Papers 1403.5599, arXiv.org.
    • Handle: RePEc:arx:papers:1403.5599
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    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
    2. Nick Webber & Claudia Ribeiro, 2003. "Valuing Path Dependent Options in the Variance-Gamma Model by Monte Carlo with a Gamma Bridge," Computing in Economics and Finance 2003 4, Society for Computational Economics.
    3. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-524, October.
    4. Chi‐Leung Lau, 1980. "A Simple Series for the Incomplete Gamma Integral," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 29(1), pages 113-114, March.
    5. G. W. Cran & K. J. Martin & G. E. Thomas, 1977. "A Remark on Algorithms," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 26(1), pages 111-114, March.
    6. K. L. Majumder & G. P. Bhattacharjee, 1973. "The Incomplete Beta Integral," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 22(3), pages 409-411, November.
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