Giacomo Toscano, Giulia Livieri, Maria Elvira Mancino, Stefano Marmi
arXiv 29 Dec 2021 · Mathematics — Statistics Theory · publishedJournal of Financial Econometrics (2022) · 12 citations (OpenAlex)
arXiv:2112.14529 · PDF · DOI · OpenAlex · Extracted main text
We study the asymptotic normality of two feasible estimators of the integrated volatility of volatility based on the Fourier methodology, which does not require the pre-estimation of the spot volatility. We show that the bias-corrected estimator reaches the optimal rate $n^{1/4}$, while the estimator without bias-correction has a slower convergence rate and a smaller asymptotic variance. Additionally, we provide simulation results that support the theoretical asymptotic distribution of the rate-efficient estimator and show the accuracy of the latter in comparison with a rate-optimal estimator based on the pre-estimation of the spot volatility. Finally, using the rate-optimal Fourier estimator, we reconstruct the time series of the daily volatility of volatility of the S&P500 and EUROSTOXX50 indices over long samples and provide novel insight into the existence of stylized facts about the volatility of volatility dynamics.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Sanfelici, S., Curato, I.V. and Mancino, M.E (2015) High frequency volatility of volatility estimation free from spot volatility estimates self | 1.000 | 10 | 3 | 100% |
| 2 | Li, Y., Liu, G. and Zhang, Z (2021) Volatility of volatility: estimation and tests based on noisy high frequency data with jumps | 1.000 | 6 | 4 | 100% |
| 3 | Vetter, M (2015) Estimation of integrated volatility of volatility with applications to goodness-of-fit testing | 1.000 | 6 | 3 | 100% |
| 4 | Aït-Sahalia, Y. and Jacod, J (2014) High-Frequency financial econometrics | 0.965 | 10 | 5 | 90% |
| 5 | Cuchiero, C. and Teichmann, J (2015) Fourier transform methods for pathwise covariance estimation in the presence of jumps | 0.928 | 5 | 4 | 80% |
| 6 | Malliavin, P. and Mancino, M.E (2002) Fourier series method for measurement of multivariate volatilities self | 0.928 | 5 | 4 | 80% |
| 7 | Livieri, G., Mancino, M.E. and Marmi, S (2019) Asymptotic results for the Fourier estimator of the integrated quarticity self | 0.843 | 5 | 4 | 60% |
| 8 | Barndorff-Nielsen, O.E. and Veraart, A (2009) Stochastic volatility of volatility in continuous time | 0.811 | 4 | 2 | 100% |
| 9 | Barucci, E. and Mancino, M.E (2010) Computation of volatility in stochastic volatility models with high frequency data self | 0.737 | 3 | 2 | 100% |
| 10 | Malliavin, P. and Mancino, M.E (2009) A Fourier transform method for nonparametric estimation of multivariate volatility self | 0.644 | 4 | 2 | 50% |
Showing the top 10 of 32 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
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| 1 | The Fourier-Malliavin Volatility (FMVol) MATLAB$^$ library | 0.644 | 2 | 2 |
| 2 | Volatility of Volatility and Leverage Effect from Options | 0.405 | 1 | 1 |