# Strong order 1/2 convergence of full truncation Euler approximations to the Cox-Ingersoll-Ross process

## TL;DR

This paper proves that the full truncation Euler scheme converges with strong order 1/2 for the Cox-Ingersoll-Ross process when the boundary zero is inaccessible, under certain parameter conditions.

## Contribution

It establishes the strong order 1/2 convergence of the full truncation Euler scheme for the CIR process in a specific parameter regime, extending understanding of numerical methods for non-Lipschitz SDEs.

## Key findings

- Strong order 1/2 convergence in $L^{p}$ established
- Convergence holds when Feller ratio exceeds three
- Results align with optimal convergence rates for Lipschitz SDEs

## Abstract

We study convergence properties of the full truncation Euler scheme for the Cox-Ingersoll-Ross process in the regime where the boundary point zero is inaccessible. Under some conditions on the model parameters (precisely, when the Feller ratio is greater than three), we establish the strong order 1/2 convergence in $L^{p}$ of the scheme to the exact solution. This is consistent with the optimal rate of strong convergence for Euler approximations of stochastic differential equations with globally Lipschitz coefficients, despite the fact that the diffusion coefficient in the Cox-Ingersoll-Ross model is not Lipschitz.