Convergence and non-negativity preserving of the solution of balanced method for the delay CIR model with jump

TL;DR

This paper introduces a balanced implicit numerical method for the delay CIR model with jumps, ensuring non-negativity, strong convergence, and bounded moments, with theoretical proofs and illustrative results.

Contribution

The paper presents a new BIM approach that preserves non-negativity and converges strongly for the delay CIR model with jumps, advancing numerical solutions for such stochastic models.

Findings

BIM preserves non-negativity of the solution.

Strong convergence of the BIM is established.

Boundedness of the p-th moments is demonstrated.

Abstract

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.