  In this paper, we study analytical properties of the solutions to the
generalised delay Ait-Sahalia-type interest rate model with Poisson-driven
jump. Since this model does not have explicit solution, we employ several new
truncated Euler-Maruyama (EM) techniques to investigate finite time strong
convergence theory of the numerical solutions under the local Lipschitz
condition plus the Khasminskii-type condition. We justify the strong
convergence result for Monte Carlo calibration and valuation of some debt and
derivative instruments.
