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

ArXiv ID: 2507.10041 “View on arXiv”

Authors: Sourojyoti Barick

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 ($α\in[“0.5,1”]$). 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 $α\in[“0.5,1”]$.

Keywords: Cox-Ingersoll-Ross (CIR), Chan-Karolyi-Longstaff-Sanders (CKLS), Stochastic Differential Equations (SDEs), Parameter Estimation, Mean Reversion, Interest Rates

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 3.5/10
• Quadrant: Lab Rats
• Why: The paper employs advanced stochastic calculus, SDE analysis, and asymptotic proofs, resulting in high mathematical density, but relies on theoretical derivations and simulations without providing ready-to-use code, datasets, or rigorous backtesting results.

  flowchart TD
    A["Research Goal:<br>Estimate Parameters & Analyze<br>Asymptotics in CIR/CKLS Models"] --> B["Methodology:<br>Euler-Maruyama Discretization of SDEs"]
    B --> C["Computational Process:<br>Linear Regression on<br>Discretized Equations"]
    C --> D{"Key Outcomes"}
    D --> E["Theoretical Guarantees:<br>Strong Consistency &<br>Asymptotic Normality"]
    D --> F["Boundary Analysis:<br>Unattainability at Zero/Infinity<br>via Scale/Speed Functions"]
    D --> G["Stationarity:<br>Existence & Density of<br>Stationary Distribution"]