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The Fourier–Malliavin Volatility (FMVol) MATLAB® library

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  • Sanfelici, Simona
  • Toscano, Giacomo

Abstract

This paper presents the Fourier–Malliavin Volatility (FMVol) estimation library for MATLAB®. This library includes functions that implement Fourier–Malliavin estimators (see Malliavin and Mancino (2002, 2009)) of the volatility and co-volatility of continuous stochastic volatility processes and second-order quantities, like the quarticity (the squared volatility), the volatility of volatility and the leverage (the covariance between changes in the process and changes in its volatility). The Fourier–Malliavin method is fully non-parametric, does not require equally-spaced observations and is robust to measurement errors, or noise, without any preliminary bias correction or pre-treatment of the observations. Furthermore, in its multivariate version, it is intrinsically robust to irregular and asynchronous sampling. Although originally introduced for a specific application in financial econometrics, namely the estimation of asset volatilities, the Fourier–Malliavin method is a general method that can be applied whenever one is interested in reconstructing the latent volatility and second-order quantities of a continuous stochastic volatility process from discrete observations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:226:y:2024:i:c:p:338-353
    DOI: 10.1016/j.matcom.2024.07.003
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    References listed on IDEAS

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    1. Giacomo Toscano & Giulia Livieri & Maria Elvira & Stefano Marmi, 2024. "Volatility of Volatility Estimation: Central Limit Theorems for the Fourier Transform Estimator and Empirical Study of the Daily Time Series Stylized Facts," Journal of Financial Econometrics, Oxford University Press, vol. 22(1), pages 252-296.
    2. Maria Elvira Mancino & Simona Sanfelici, 2012. "Estimation of quarticity with high-frequency data," Quantitative Finance, Taylor & Francis Journals, vol. 12(4), pages 607-622, December.
    3. Patrick Chang & Etienne Pienaar & Tim Gebbie, 2020. "Malliavin-Mancino estimators implemented with non-uniform fast Fourier transforms," Papers 2003.02842, arXiv.org, revised Nov 2020.
    4. Simona Sanfelici & Imma Valentina Curato & Maria Elvira Mancino, 2015. "High-frequency volatility of volatility estimation free from spot volatility estimates," Quantitative Finance, Taylor & Francis Journals, vol. 15(8), pages 1331-1345, August.
    5. Yacine Aït-Sahalia & Jean Jacod, 2014. "High-Frequency Financial Econometrics," Economics Books, Princeton University Press, edition 1, number 10261.
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    7. Maria Elvira Mancino & Simona Sanfelici, 2011. "Estimating Covariance via Fourier Method in the Presence of Asynchronous Trading and Microstructure Noise," Journal of Financial Econometrics, Oxford University Press, vol. 9(2), pages 367-408, Spring.
    8. Maria Elvira Mancino & Simona Sanfelici, 2011. "Covariance Estimation and Dynamic Asset-Allocation under Microstructure Effects via Fourier Methodology," Palgrave Macmillan Books, in: Greg N. Gregoriou & Razvan Pascalau (ed.), Financial Econometrics Modeling: Market Microstructure, Factor Models and Financial Risk Measures, chapter 1, pages 3-32, Palgrave Macmillan.
    9. Giulia Livieri & Maria Elvira Mancino & Stefano Marmi, 2019. "Asymptotic results for the Fourier estimator of the integrated quarticity," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(2), pages 471-502, December.
    10. Mancino, M.E. & Sanfelici, S., 2008. "Robustness of Fourier estimator of integrated volatility in the presence of microstructure noise," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 2966-2989, February.
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    13. Giacomo Toscano & Maria Cristina Recchioni, 2020. "Bias optimal vol-of-vol estimation: the role of window overlapping," Papers 2004.04013, arXiv.org, revised Jul 2021.
    14. Curato, Imma Valentina & Sanfelici, Simona, 2022. "Stochastic leverage effect in high-frequency data: a Fourier based analysis," Econometrics and Statistics, Elsevier, vol. 23(C), pages 53-82.
    15. Curato, Imma Valentina, 2019. "Estimation of the stochastic leverage effect using the Fourier transform method," Stochastic Processes and their Applications, Elsevier, vol. 129(9), pages 3207-3238.
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    18. 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.
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