On explicit numerical schemes for the CIR process

TL;DR

This paper introduces and analyzes new explicit numerical schemes for the CIR process, improving positivity preservation, convergence properties, and extending to two-factor models with exact simulation techniques.

Contribution

It generalizes an existing explicit scheme for the CIR process, enhancing positivity preservation and convergence, and develops new schemes for two-factor CIR models using exact simulation.

Findings

The new scheme preserves positivity for a broader parameter set.

Convergence order is at least logarithmic, improved to 1/4 for certain parameters.

The paper successfully applies schemes to two-factor CIR models.

Abstract

In this paper we generalize an explicit numerical scheme for the CIR process that we have proposed before. The advantage of the new proposed scheme is that preserves positivity and is well posed for a (little bit) broader set of parameters among the positivity preserving schemes. The order of convergence is at least logarithmic in general and for a smaller set of parameters is at least $1/4$. Next we give a different explicit numerical scheme based on exact simulation and we use this idea to approximate the two factor CIR model. Finally, we give a second explicit numerical scheme for the two factor CIR model based on the idea of the second section.