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We demonstrate the effectiveness of an adaptive explicit Euler method for theapproximate solution of the Cox-Ingersoll-Ross model. This relies on a class ofpath-bounded timestepping strategies which work by reducing the stepsize assolutions approach a neighbourhood of zero. The method is hybrid in the sensethat a convergent backstop method is invoked if the timestep becomes too small,or to prevent solutions from overshooting zero and becoming negative. Underparameter constraints that imply Feller's condition, we prove that such ascheme is strongly convergent, of order at least 1/2. Control of the strongerror is important for multi-level Monte Carlo techniques. Under Feller'scondition we also prove that the probability of ever needing the backstopmethod to prevent a negative value can be made arbitrarily small. Numerically,we compare this adaptive method to fixed step implicit and explicit schemes,and a novel semi-implicit adaptive variant. We observe that the adaptiveapproach leads to methods that are competitive in a domain that extends beyondFeller's condition, indicating suitability for the modelling of stochasticvolatility in Heston-type asset models.

The role of adaptivity in a numerical method for the Cox-Ingersoll-Ross model