A pathwise inference method for the parameters of diffusion terms

TL;DR

This paper introduces a novel pathwise inference method for estimating the parameters of diffusion terms in processes like Cox-Ingersoll-Ross, using auxiliary complex processes to avoid distributional assumptions.

Contribution

It proposes original pathwise estimates for diffusion coefficients and power indices that do not depend on the process distribution or drift choice.

Findings

Estimates are feasible and effective in numerical experiments.

Method does not rely on distributional assumptions.

Applicable to Cox-Ingersoll-Ross and similar processes.

Abstract

We consider inference of the parameters of the diffusion term for Cox-Ingersoll-Ross and similar processes with a power type dependence of the diffusion coefficient from the underlying process. We suggest some original pathwise estimates for this coefficient and for the power index based on an analysis of an auxiliary continuous time complex valued process generated by the underlying real valued process. These estimates do not rely on the distribution of the underlying process and on a particular choice of the drift. Some numerical experiments are used to illustrate the feasibility of the suggested method.