2022/09/19 by Maria Elvira Mancino, Mancino, Maria Elvira, Tommaso Mariotti +3 · 2 citations
Economics, Econometrics and Finance · Mathematics · #FOS: Economics and business #Statistical Finance (q-fin.ST) #Statistical Methods and Inference #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2209.08967
openalex publication_date 2022/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The main contribution of the paper is proving that the Fourier spot volatility estimator introduced in [Malliavin and Mancino, 2002] is consistent and asymptotically efficient if the price process is contaminated by microstructure noise. Specifically, in the presence of additive microstructure noise we prove a Central Limit Theorem with the optimal rate of convergence n1/8. The result is obtained without the need for any manipulation of the original data or bias correction. Moreover, we complete the asymptotic theory for the Fourier spot volatility estimator in the absence of noise, originally presented in [Mancino and Recchioni, 2015], by deriving a Central Limit Theorem with the optimal convergence rate n1/4. Finally, we propose a novel feasible adaptive method for the optimal selection of the parameters involved in the implementation of the Fourier spot volatility estimator with noisy high-frequency data and provide support to its accuracy both numerically and empirically.