Alternative methods for simulating square root processes

Square root processes are used in quantitative finance to model state variables that are non-negative. Applications include models for stochastic volatility, stochastic credit spreads, and strictly non-negative interest rates. Applications for derivative pricing typically require simulation of stochastic processes, including the square root process. The purpose of this paper is to revisit methods for fast simulation of square root process to be applied with parallel processing. The paper reviews the square root process and a variety of simulation methods, including the simulation of the non-central chi squared distribution, the exact distribution for the process over discrete time intervals. Simulation methods for the non-central chi squared distribution are relatively slow and not well-suited for simulation in dynamic financial models. Alternative approximation methods are developed, and a battery of goodness-of-fit statistical tests are applied to the alternative methods. The paper includes discussion of random number generation for the purpose of simulating square root processes across parallel processors. The alternative simulation methods require only one uniform random number generator per time step and facilitate hedging and parameter calibration with parallel processing. The test results indicate that the approximation methods generally converge and significantly reduce computing time when parallel processing is applied on a GPU.