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Fourier Spot Volatility Estimator: Asymptotic Normality and Efficiency with Liquid and Illiquid High-Frequency Data

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  • Maria Elvira Mancino
  • Maria Cristina Recchioni

Abstract

The recent availability of high frequency data has permitted more efficient ways of computing volatility. However, estimation of volatility from asset price observations is challenging because observed high frequency data are generally affected by noise-microstructure effects. We address this issue by using the Fourier estimator of instantaneous volatility introduced in Malliavin and Mancino 2002. We prove a central limit theorem for this estimator with optimal rate and asymptotic variance. An extensive simulation study shows the accuracy of the spot volatility estimates obtained using the Fourier estimator and its robustness even in the presence of different microstructure noise specifications. An empirical analysis on high frequency data (U.S. S&P500 and FIB 30 indices) illustrates how the Fourier spot volatility estimates can be successfully used to study intraday variations of volatility and to predict intraday Value at Risk.

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  • Maria Elvira Mancino & Maria Cristina Recchioni, 2015. "Fourier Spot Volatility Estimator: Asymptotic Normality and Efficiency with Liquid and Illiquid High-Frequency Data," PLOS ONE, Public Library of Science, vol. 10(9), pages 1-33, September.
    • Handle: RePEc:plo:pone00:0139041
    DOI: 10.1371/journal.pone.0139041
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    Cited by:

    1. Maria Elvira Mancino & Tommaso Mariotti & Giacomo Toscano, 2022. "Asymptotic Normality for the Fourier spot volatility estimator in the presence of microstructure noise," Papers 2209.08967, arXiv.org.
    2. Sanfelici, Simona & Toscano, Giacomo, 2024. "The Fourier–Malliavin Volatility (FMVol) MATLAB® library," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 226(C), pages 338-353.
    3. Elisa Alòs & Maria Elvira Mancino & Tai-Ho Wang, 2019. "Volatility and volatility-linked derivatives: estimation, modeling, and pricing," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(2), pages 321-349, December.
    4. Alessio Brini & Giacomo Toscano, 2024. "SpotV2Net: Multivariate Intraday Spot Volatility Forecasting via Vol-of-Vol-Informed Graph Attention Networks," Papers 2401.06249, arXiv.org, revised Jan 2025.
    5. Recchioni, Maria Cristina & Tedeschi, Gabriele, 2017. "From bond yield to macroeconomic instability: A parsimonious affine model," European Journal of Operational Research, Elsevier, vol. 262(3), pages 1116-1135.
    6. M.E. Mancino & S. Scotti & G. Toscano, 2020. "Is the Variance Swap Rate Affine in the Spot Variance? Evidence from S&P500 Data," Applied Mathematical Finance, Taylor & Francis Journals, vol. 27(4), pages 288-316, July.
    7. Simona Sanfelici & Giacomo Toscano, 2024. "The Fourier-Malliavin Volatility (FMVol) MATLAB library," Papers 2402.00172, arXiv.org.
    8. Curato, Imma Valentina & Mancino, Maria Elvira & Recchioni, Maria Cristina, 2018. "Spot volatility estimation using the Laplace transform," Econometrics and Statistics, Elsevier, vol. 6(C), pages 22-43.
    9. Patrick Chang, 2020. "Fourier instantaneous estimators and the Epps effect," Papers 2007.03453, arXiv.org, revised Sep 2020.
    10. Richard Y. Chen, 2019. "The Fourier Transform Method for Volatility Functional Inference by Asynchronous Observations," Papers 1911.02205, arXiv.org.
    11. Maria Cristina Recchioni & Gabriele Tedeschi, 2016. "From bond yield to macroeconomic instability: The effect of negative interest rates," Working Papers 2016/06, Economics Department, Universitat Jaume I, Castellón (Spain).

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