  In this work, we propose the balanced implicit method (BIM) to approximate
the solution of the delay Cox-Ingersoll-Ross (CIR) model with jump which often
gives rise to model an asset price and stochastic volatility . We show that
this method preserves non-negativity property of the solution of this model
with appropriate control functions. We prove the strong convergence and
investigate the $p$th moment boundedness of the solution of BIM. Finally, we
illustrate those results in the last section.
