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

Abstract: 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.