On the numerical stability of strong predictor-corrector Euler schemes for SDEs

When simulating discrete-time approximations of solutions of SDEs, numerical stability is clearly more important than higher order of convergence. Discrete time approximations of solutions of SDEs are widely used in simulations in finance and other areas of application. The stability criterion is presented and stability regions for various schemes are visualized. The result is that schemes, which have implicitness in both the drift and the diffusion terms, exhibit the largest stability regions. Refining the time step size in a simulation can lead to numerical instabilities, which is not what one experiences in deterministic numerical analysis. The symmetric predictor-corrector Euler method is shown to have the potential to overcome some of the numerical instabilities that may be experienced when using the explicit Euler method.