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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

Comparison of the autocorrelation functions.Autocorrelation function of a sampled normal process e(0, Δ t) with sampling interval of 1 minute (upper panel) and of the 1-minute returns observed on March 4, 2013 (lower panel).
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pone.0139041.g008: Comparison of the autocorrelation functions.Autocorrelation function of a sampled normal process e(0, Δ t) with sampling interval of 1 minute (upper panel) and of the 1-minute returns observed on March 4, 2013 (lower panel).

Mentions: Fig 8 shows the autocorrelation function of a sampled Gaussian distribution (0, Δ t) with sampling frequency of 1-minute (upper panel) and the autocorrelation of 1-minute observed returns on March 4, 2013 (lower panel). The results shown in the two panels and the preliminary analysis illustrated above suggest the use of 1-minute returns in order to reconstruct the distribution of the standardized return zt, defined in Eq (14). As previously mentioned, the standardized return, zt, is a standard Gaussian random variable when the prices are not affected by microstructure noise effects.


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

Mancino ME, Recchioni MC - PLoS ONE (2015)

Comparison of the autocorrelation functions.Autocorrelation function of a sampled normal process e(0, Δ t) with sampling interval of 1 minute (upper panel) and of the 1-minute returns observed on March 4, 2013 (lower panel).
© Copyright Policy
Related In: Results  -  Collection

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

pone.0139041.g008: Comparison of the autocorrelation functions.Autocorrelation function of a sampled normal process e(0, Δ t) with sampling interval of 1 minute (upper panel) and of the 1-minute returns observed on March 4, 2013 (lower panel).
Mentions: Fig 8 shows the autocorrelation function of a sampled Gaussian distribution (0, Δ t) with sampling frequency of 1-minute (upper panel) and the autocorrelation of 1-minute observed returns on March 4, 2013 (lower panel). The results shown in the two panels and the preliminary analysis illustrated above suggest the use of 1-minute returns in order to reconstruct the distribution of the standardized return zt, defined in Eq (14). As previously mentioned, the standardized return, zt, is a standard Gaussian random variable when the prices are not affected by microstructure noise effects.

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