Exponential ergodicity of an affine two-factor model based on the $\alpha$-root process

TL;DR

This paper proves that a specific two-factor affine model, which includes a generalized CIR process, exhibits exponential ergodicity for certain parameter ranges, enhancing understanding of its long-term behavior.

Contribution

The paper establishes exponential ergodicity for an affine two-factor model with an alpha-root process, extending previous results to a broader class of models.

Findings

Model is exponentially ergodic for alpha in (1,2)

Generalizes the CIR process within the affine framework

Provides conditions for stability and long-term behavior

Abstract

We study an affine two-factor model introduced by Barczy et al. (2014). One component of this two-dimensional model is the so-called $\alpha$-root process, which generalizes the well known CIR process. In this paper, we show that this affine two-factor model is exponentially ergodic when $\alpha\in(1,2)$.