  For Ait-Sahalia-type interest rate model with Poisson jumps, we are
interested in strong convergence of a novel time-stepping method, called
transformed jump-adapted backward Euler method (TJABEM). Under certain
hypothesis, the considered model takes values in positive domain $(0,\infty)$.
It is shown that the TJABEM can preserve the domain of the underlying problem.
Furthermore, for the above model with non-globally Lipschitz drift and
diffusion coefficients, the strong convergence rate of order one of the TJABEM
is recovered with respect to a $L^p$-error criterion. Finally, numerical
experiments are given to illustrate the theoretical results.
