Positivity and convergence of the balanced implicit method for the nonlinear jump-extended CIR model

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 L 1 and L 2 sense. Finally, we give two examples to illustrate the positivity and convergence of the BIM; numerical results verify the theoretical findings.