Preserving non-negativity and convergence analysis of the balanced implicit method for the delay-Heston model

In this paper, we propose a new delay-Heston model, in which the delay Cox-Ingersoll-Ross (CIR) model is used to represent volatility of the Heston model. The delay-Heston model has non-negative solution. We propose the balanced implicit method (BIM) for this model. We determine control functions of the BIM such that this method can preserve non-negativity of true solution of the model. We prove strong convergence of the BIM.