Asymptotic Normality and Finite-Sample Robustness of the Fourier Spot Volatility Estimator in the Presence of Microstructure Noise
微观结构噪声下傅里叶瞬时波动率估计的渐近正态性与有限样本稳健性
We study the efficiency and robustness of the Fourier spot volatility estimator when high-frequency prices are contaminated by microstructure noise. First, we show that the estimator is consistent and asymptotically efficient in the presence of additive noise, establishing a Central Limit Theorem (CLT) with the optimal rate of convergence n1/8. Additionally, we complete the asymptotic theory in the absence of noise, obtaining a CLT with the optimal rate of convergence n1/4.…