  We prove mean-square convergence of a novel numerical method, the
tamed-splitting method, for a generalized Ait-Sahalia interest rate model. The
method is based on a Lamperti transform, splitting and applying a tamed
numerical method for the nonlinearity. The main difficulty in the analysis is
caused by the non-globally Lipschitz drift coefficients of the model. We
examine the existence, uniqueness of the solution and boundedness of moments
for the transformed SDE.We then prove bounded moments and inverses moments for
the numerical approximation. The tamed-splitting method is a hybrid method in
the sense that a backstop method is invoked to prevent solutions from
overshooting zero and becoming negative. We successfully recover the
mean-square convergence rate of order one for the tamed-splitting method. In
addition we prove that the probability of ever needing the backstop method to
prevent a negative value can be made arbitrarily small. In our numerical
experiments we compare to other numerical methods in the literature for
realistic parameter values.
