Moderate deviations for parameters estimation in a geometrically ergodic Heston process

TL;DR

This paper proves a moderate deviation principle for maximum likelihood estimators of parameters in a geometrically ergodic Heston process and a generalized squared radial Ornstein-Uhlenbeck process, with simultaneous parameter estimation.

Contribution

It introduces the first moderate deviation results for simultaneous parameter estimation in these stochastic processes under specific ergodicity conditions.

Findings

Established moderate deviation principles for the estimators.

Extended results to a generalized squared radial Ornstein-Uhlenbeck process.

Parameters estimated simultaneously, contrasting with previous literature.

Abstract

We establish a moderate deviation principle for the maximum likelihood estimator of the four parameters of a geometrically ergodic Heston process. We also obtain moderate deviations for the maximum likelihood estimator of the couple of dimensional and drift parameters of a generalized squared radial Ornstein-Uhlenbeck process. We restrict ourselves to the most tractable case where the dimensional parameter satisfies $a>2$ and the drift coefficient is such that $b<0$. In contrast to the previous literature, parameters are estimated simultaneously.