First order strong approximation of Ait–Sahalia-type interest rate model with Poisson jumps

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 hypotheses, the considered model takes values in positive domain. It is shown that the TJABEM can preserve the domain of the underlying problem. Furthermore, the first-order convergence rate of the TJABEM is recovered with respect to a L p -error criterion. Numerical experiments are finally given to illustrate the theoretical results.