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

Mancino ME, Recchioni MC - PLoS ONE (2015)

Bottom Line: The recent availability of high frequency data has permitted more efficient ways of computing volatility.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.

View Article: PubMed Central - PubMed

Affiliation: Department of Economics and Management, University of Florence, Florence, Italy.

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.

No MeSH data available.


Related in: MedlinePlus

Autocorrelation functions.The four panels show the autocorrelation in 5-second returns (March 4-7, 2013).
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pone.0139041.g006: Autocorrelation functions.The four panels show the autocorrelation in 5-second returns (March 4-7, 2013).

Mentions: This finding is confirmed by Figs 6 and 7. Fig 6 shows the 5-second return autocorrelation function on March 4-7, 2013 while Fig 7 shows the autocorrelation function of the returns on March 4, 2013 for four different sampling frequencies (i.e. upper left panel 5-second returns, upper right panel 10-second returns, lower left panel 30-second returns and lower right panel 1-minute returns). These two figures show a positive serial autocorrelation at high frequencies and this implies smaller estimates of the realized variance for these frequencies. As stressed in Ref. [25], high quality realized variance estimates can be constructed in a liquid market. However, we investigate the performance of the Fourier estimator also against illiquid assets.


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

Mancino ME, Recchioni MC - PLoS ONE (2015)

Autocorrelation functions.The four panels show the autocorrelation in 5-second returns (March 4-7, 2013).
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4589382&req=5

pone.0139041.g006: Autocorrelation functions.The four panels show the autocorrelation in 5-second returns (March 4-7, 2013).
Mentions: This finding is confirmed by Figs 6 and 7. Fig 6 shows the 5-second return autocorrelation function on March 4-7, 2013 while Fig 7 shows the autocorrelation function of the returns on March 4, 2013 for four different sampling frequencies (i.e. upper left panel 5-second returns, upper right panel 10-second returns, lower left panel 30-second returns and lower right panel 1-minute returns). These two figures show a positive serial autocorrelation at high frequencies and this implies smaller estimates of the realized variance for these frequencies. As stressed in Ref. [25], high quality realized variance estimates can be constructed in a liquid market. However, we investigate the performance of the Fourier estimator also against illiquid assets.

Bottom Line: The recent availability of high frequency data has permitted more efficient ways of computing volatility.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.

View Article: PubMed Central - PubMed

Affiliation: Department of Economics and Management, University of Florence, Florence, Italy.

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.

No MeSH data available.


Related in: MedlinePlus