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Accuracy and precision of parallel Monte Carlo (MC) simulations may be impaired by the presence of intra-thread and inter-thread correlations depending on the parallel pseudo-random number generators (PPRNGs) used. While necessary, statistical tests alone are insufficient to ensure the absence of these correlations that can manifest as bias and variance to a extent in different applications. Therefore, application-based tests designed to mimic real-life MC scenarios may uncover them in the intended applications. The results of an application-based test simulating the Heston stochastic volatility model, a widely used pricing framework, is reported in order to compare the accuracy and precision profiles among four popular libraries of scalable pseudo-random number generators implementing sequence division ( trng  and  RngSteam ), parameterization ( sprng ) and counter-based ( Random123 ) strategies. All pseudo-random number generators assessed demonstrate similar standard-error of mean profiles. However, the bias profiles are more varied albeit comparable. PPRNGs demonstrating the smallest bias profiles in absolute and relative terms are  yarn4  from  TRNG ,  mlfg  from  SPRNG , as well as  Threefry2x64  from  Random123  for truncated Euler scheme, and  mrg5s  from  TRNG  and  lfg  from  SPRNG  for the quadratic exponent scheme. It is recommended that, when selecting a PPRNG for parallel MC simulation from a set of competing PPRNGs with comparable bias and standard error of mean profiles in absolute terms, the PPRNG associated with the smallest parallel-sequential bias difference should be used as it reflects the smallest intra-thread correlation introduced by parallelization.

Parallel pseudo-random number generators: A derivative pricing perspective with the Heston stochastic volatility model