On the ergodicity of a three-factor CIR model

TL;DR

This paper establishes the Wasserstein ergodicity of a novel three-factor CIR model with correlated stochastic trends and volatilities, using advanced mathematical techniques beyond traditional methods, and applies these results to the Chen model.

Contribution

It introduces a new three-factor CIR model and develops novel mathematical methods to prove its Wasserstein ergodicity, extending to the Chen model.

Findings

Proved Wasserstein ergodicity of the CIR3 model.

Developed alternative mathematical approaches for ergodicity.

Extended methods to the Chen model.

Abstract

This study introduces the CIR3 model, a three-factor model characterized by stochastic and correlated trends and volatilities. The paper focuses on establishing the Wasserstein ergodicity of this model, a task not achievable through conventional means such as the Dobrushin theorem. Instead, alternative mathematical approaches are employed, including considerations of topological aspects of Wasserstein spaces and Kolmogorov equations for measures. Remarkably, the methodology developed here can also be applied to prove the Wasserstein ergodicity of the widely recognized three-factor Chen model.