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

Abstract

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.