Abstract
In this paper, we extend the balanced implicit method (BIM) to nonlinear jump-extended Cox–Ingersoll–Ross (CIR) model. Firstly, we construct the numerical method BIM for this nonlinear jump-extended CIR model and prove the positivity of the proposed method for the model. Furthermore the strong convergence of the BIM is proved in L1 and L2 sense. Finally, we give two examples to illustrate the positivity and convergence of the BIM; numerical results verify the theoretical findings.
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