Maximum Likelihood Estimation for Wishart processes

TL;DR

This paper investigates the maximum likelihood estimation of drift parameters in Wishart processes, providing convergence rates and limits, and extends related Laplace transform results relevant for financial modeling.

Contribution

It offers new theoretical results on the MLE's convergence behavior for Wishart processes and extends Laplace transform findings, enhancing parameter estimation methods.

Findings

MLE achieves optimal convergence rates in ergodic and nonergodic cases

Precise convergence limits for the MLE are established

New Laplace transform results extend existing theoretical frameworks

Abstract

In the last decade, there has been a growing interest to use Wishart processes for modelling, especially for financial applications. However, there are still few studies on the estimation of its parameters. Here, we study the Maximum Likelihood Estimator (MLE) in order to estimate the drift parameters of a Wishart process. We obtain precise convergence rates and limits for this estimator in the ergodic case and in some nonergodic cases. We check that the MLE achieves the optimal convergence rate in each case. Motivated by this study, we also present new results on the Laplace transform that extend the recent findings of Gnoatto and Grasselli and are of independent interest.