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

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 derivatives 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, together 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.