Numerical recipes in C: the art of scientific computing
Numerical recipes in C: the art of scientific computing
Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Quasi-random sequences and their discrepancies
SIAM Journal on Scientific Computing
Randomized algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Parameterization based on randomized quasi-Monte Carlo methods
Parallel Computing
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Recently, Paskov reported that, the use of a certain pseudo-random number generator, ran1() which is 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 also present a method for avoiding such wrong convergences. A variance reduction procedure is applied together with the method to obtain more precise value, and the effectiveness is examined.