Parallel random number generators in Monte Carlo derivative pricing: An application-based test

Parallel pseudorandom number generators (PPRNG) that satisfy classical statistical tests may still demonstrate intra-stream and inter-stream correlations in real life applications. In order to investigate the suitability of a PPRNG for use in Monte Carlo pricing of financial derivatives, an application-based test is proposed to evaluate the bias and the standard error of the mean (SE) associated with the PPRNG as a gauge of intrastream and inter-stream correlations respectively. This test involves estimating the price of a vanilla European call option via Monte Carlo simulation, where the asset price at maturity is estimated by propagating the Black–Scholes stochastic differential equation via the Euler–Maruyama discretization scheme. The mean and SE profiles of the numerical results based on three PPRNG libraries (RNGSTREAM, TRNG and SPRNG) that implement parallel random numbers via sequence splitting strategies (RNGSTREAM and TRNG) and parameterization strategy (SPRNG) are compared. In terms of the bias and SE profiles, the best performing PPRNG constructed using the sequence splitting strategy is comparable to that constructed using parameterization, both use multiple recursive generators in their kernel.