An Accurate Discretized Approach to Parameter Estimation in the CKLS Model via the CIR Framework

TL;DR

This paper introduces a discretized estimation method for the CKLS interest rate model, extending the CIR framework, and proves the consistency and asymptotic normality of the estimators.

Contribution

It develops a new discretized approach using Euler-Maruyama for parameter estimation in the CKLS model, with theoretical guarantees and analysis of boundary behaviors.

Findings

Establishes strong consistency of estimators.

Proves asymptotic normality of estimators.

Derives conditions for stationary distribution existence.

Abstract

This paper provides insight into the estimation and asymptotic behavior of parameters in interest rate models, focusing primarily on the Cox-Ingersoll-Ross (CIR) process and its extension -- the more general Chan-Karolyi-Longstaff-Sanders (CKLS) framework ($\alpha\in[0.5,1]$). The CIR process is widely used in modeling interest rates which possess the mean reverting feature. An Extension of CIR model, CKLS model serves as a foundational case for analyzing more complex dynamics. We employ Euler-Maruyama discretization to transform the continuous-time stochastic differential equations (SDEs) of these models into a discretized form that facilitates efficient simulation and estimation of parameters using linear regression techniques. We established the strong consistency and asymptotic normality of the estimators for the drift and volatility parameters, providing a theoretical underpinning for the parameter estimation process. Additionally, we explore the boundary behavior of these models, particularly in the context of unattainability at zero and infinity, by examining the scale and speed density functions associated with generalized SDEs involving polynomial drift and diffusion terms. Furthermore, we derive sufficient conditions for the existence of a stationary distribution within the CKLS framework and the corresponding stationary density function; and discuss its dependence on model parameters for $\alpha\in[0.5,1]$.