Analysis of the anomaly of ran1() generator in Monte Carlo pricing of financial derivatives

Abstract

Recently, Paskov reported that the use of a certain pseudo-random number generator, ran1(), given in Numerical Recipes in C, First Edition makes Monte Carlo simulations for pricing financial deriva-tives converge to wrong values. In this paper, we trace Paskov's experiment, investigate the characteristics and the generation algorithm of the pseudo-random number generator in question, and explain why the wrong convergences occur. We then present a method for avoiding such wrong convergences. A variance reduction procedure is applied, to gether with a method for obtaining more precise values, and its correctness is examined. We also investigate whether statistical tests for pseudo-random numbers can detect the cause of wrong convergences.