Maximum likelihood type estimation for discretely observed CIR model with small $\alpha$-stable noises

TL;DR

This paper develops a maximum likelihood type estimation method for the parameters of a CIR model driven by alpha-stable noises, analyzing its behavior as noise dispersion diminishes and observation frequency increases.

Contribution

It introduces a novel estimation approach for CIR models with alpha-stable noises under small noise and high-frequency observation regimes.

Findings

Establishes asymptotic properties of the estimator as noise diminishes.

Provides consistency and possibly asymptotic normality results.

Extends classical CIR estimation to non-Gaussian stable noise settings.

Abstract

A maximum likelihood type estimation of the drift and volatility coefficient parameters in the CIR type model driven by $\alpha$-stable noises is studied when the dispersion parameter $\varepsilon\to0$ and the discrete observations frequency $n\to\infty$ simultaneously.