Existence results for the Cox-Ingersoll-Ross model with variable exponent diffusion

TL;DR

This paper introduces a generalized Cox-Ingersoll-Ross model with a state-dependent variable exponent diffusion, analyzing its mathematical properties and comparing different stochastic calculus interpretations, supported by numerical experiments.

Contribution

It presents a novel stochastic model with variable exponent diffusion, extending the classical CIR model and providing theoretical and numerical analysis of its properties.

Findings

Existence and uniqueness of solutions established.

Higher moment properties analyzed.

Numerical experiments validate the model's effectiveness.

Abstract

This study proposes a new stochastic model where the diffusion coefficient involves a state-dependent variable exponent function $p(\cdot)$. This new theoretically flexible framework generalizes the classical Cox-Ingersol-Ross model. The existence, uniqueness, and higher moment properties of solutions are analyzed. The validity and efficiency of the model is illustrated with numerical experiments. Finally, a detailed analysis for It\^o vs Stratonovich interpretations of the proposed model is provided.