Distributional Deviations in Random Number Generation in Finance

This paper points out that pseudo-random number generators in widely used standard software can generate severe distributional deviations from targeted distributions when used in parallel implementations. In Monte Carlo simulation of random walks for financial applications this can lead to remarkable errors. These are not reduced when increasing the sample size. The paper suggests to use instead of standard routines, combined feedback shift register methods for generating random bits in parallel that are based on particular polynomials of degree twelve. As seed numbers the use of natural random numbers is suggested. The resulting hybrid random bit generators are then suitable for parallel implementation with random walk type applications. They show better distributional properties than those typically available and can produce massive streams of random numbers in parallel, suitable for Monte Carlo simulation in finance.