Exponential integrability properties of Euler discretization schemes for the Cox-Ingersoll-Ross process

TL;DR

This paper investigates the exponential integrability of the Cox-Ingersoll-Ross process and its Euler discretizations, establishing conditions under which numerical schemes preserve key properties essential for financial modeling.

Contribution

It demonstrates that both implicit and explicit Euler schemes maintain exponential integrability of the CIR process across various parameters, providing bounds on explosion times.

Findings

Euler schemes preserve exponential integrability for the CIR process.

Lower bounds on explosion times are established.

Results support the reliability of numerical methods in financial applications.

Abstract

We analyze exponential integrability properties of the Cox-Ingersoll-Ross (CIR) process and its Euler discretizations with various types of truncation and reflection at 0. These properties play a key role in establishing the finiteness of moments and the strong convergence of numerical approximations for a class of stochastic differential equations arising in finance. We prove that both implicit and explicit Euler-Maruyama discretizations for the CIR process preserve the exponential integrability of the exact solution for a wide range of parameters, and find lower bounds on the explosion time.