Elasticity estimation via the CKLS--CIR transform for small-noise CEV-type diffusions

2026-10-05

AI Summary

This study addresses the challenging problem of estimating the elasticity parameter in small-noise CEV diffusion processes with absorbing boundaries. To this end, it proposes a feasible two-step estimator that introduces a novel Lamperti-based CKLS-CIR transformation strategy, effectively converting the nonlinear elasticity parameter into a linear drift parameter. The inference procedure further integrates Girsanov measure changes with localized realized variance techniques. As key contributions, the consistency of the proposed estimator is rigorously established, and a central limit theorem (CLT) with an explicit asymptotic variance is derived. Collectively, this work provides an efficient theoretical framework and robust methodological support for parametric inference in such complex stochastic processes.

Abstract

We construct a feasible two-step estimator for the elasticity parameter in small-noise CEV-type diffusions. Under joint small-noise and high-frequency asymptotics, we establish its consistency and an $\varepsilon^{-1}$ central limit theorem with an explicit asymptotic variance. We adapt a Lamperti-based transformation strategy to elasticity inference for a CEV process with an attainable, absorbing $0$ boundary. Under a local-to-CEV scaling, an auxiliary CKLS process and a Girsanov change of measure yield a strictly positive CIR-type benchmark in which the elasticity is recast as a linear-drift parameter. A preliminary elasticity estimator based on local realized variance supplies the unknown parameter in the state mapping, yielding a feasible LSE-type estimator. The asymptotic theory combines control of the CKLS-to-CEV path-replacement error, total-variation closeness between the original and changed measures, and asymptotic negligibility of the preliminary plug-in error, thereby transferring the auxiliary CIR limit theory to the feasible estimator under the original measure.

Problem

• elasticity estimation
• small-noise CEV-type diffusions
• high-frequency asymptotics
• elasticity parameter

Innovation

• small-noise CEV diffusions
• CKLS-CIR transform
• Lamperti transformation
• Girsanov change of measure
• two-step estimator