Inference in the stochastic Cox-Ingersol-Ross diffusion process with continuous sampling: Computational aspects and simulation

TL;DR

This paper analyzes the inference process for the Cox-Ingersoll-Ross diffusion model with continuous data, focusing on computational methods for parameter estimation and simulation of the process.

Contribution

It introduces methods for parameter estimation in the CIR model using maximum likelihood and diffusion coefficient approximation with continuous sampling.

Findings

Derived analytical trend functions using Itô's calculus.

Implemented maximum likelihood estimation for drift parameters.

Simulated trajectories demonstrating the estimation procedures.

Abstract

In this paper, we consider a stochastic model based on the Cox- Ingersoll- Ross model (CIR). The stochastic model is parameterized analytically by applying It\^o's calculus and the trend functions of the proposed process is calculated. The parameter estimators are then derived by means of two procedures: the first is used to estimate the parameters in the drift coefficient by the maximum likelihood (ML) method, based on continuous sampling, and the second procedure approximates the diffusion coefficient by two methods. Finally, a simulation of the process is presented. Thus, a typical simulated trajectory of the process and its estimators is obtained.