通过CKLS--CIR变换对小型噪声CEV型扩散的弹性估计
Elasticity estimation via the CKLS--CIR transform for small-noise CEV-type diffusions
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中文总结 AI 辅助
针对小噪声CEV型扩散，提出基于CKLS-CIR变换的两步弹性估计器，证明其一致性与中心极限定理，并通过辅助CIR过程转移极限理论。
中文摘要 AI 辅助
我们为小型噪声CEV型扩散中的弹性参数构建了一个可行的两步估计器。在联合小噪声和高频渐近条件下，我们建立了其一致性以及一个具有显式渐近方差的$\varepsilon^{-1}$中心极限定理。我们将基于Lamperti的变换策略适应于具有可达、吸收$0$边界的CEV过程的弹性推断。在局部到CEV的缩放下，辅助CKLS过程和Girsanov测度变换产生一个严格正的CIR型基准，其中弹性被重新表述为线性漂移参数。基于局部已实现方差的初步弹性估计器提供了状态映射中的未知参数，从而产生一个可行的LSE型估计器。渐近理论结合了对CKLS到CEV路径替换误差的控制、原始测度与变换测度之间的全变差接近性以及初步插入误差的渐近可忽略性，从而将辅助CIR极限理论转移到原始测度下的可行估计器。
英文摘要
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.
发表机构
- Waseda University（早稻田大学）
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