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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

Empirical distribution of the normalized asymptotic error for various sampling intervals.The panels show the empirical distribution of  for t ≈ 0.5 and c = 1/2 using 1-second returns (left upper panel), 30-second returns (right upper panel), 1-minute returns (left lower panel) 5-minute returns (right lower panel).
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pone.0139041.g002: Empirical distribution of the normalized asymptotic error for various sampling intervals.The panels show the empirical distribution of for t ≈ 0.5 and c = 1/2 using 1-second returns (left upper panel), 30-second returns (right upper panel), 1-minute returns (left lower panel) 5-minute returns (right lower panel).

Mentions: We also try to determine the largest price frequency still capable of fitting satisfactorily the theoretical distribution prescribed by Theorem 3.1. We repeat the previous experiment choosing the Nyquist frequency N = n/2 and which are shown to reduce the variance and a sampling interval of ten seconds (i.e. n = 23400/10), thirty seconds (i.e. n = 23400/30), one minute (i.e. n = 23400/60) and five minutes (i.e. n = 23400/300). We evaluate the empirical distribution at t ≈ 0.5 and we apply the Bera-Jarque test at the significance level of 0.05. The empirical and theoretical distributions are shown in Fig 2. We can observe that when the sampling interval increases from ten seconds to one minute (upper panels and left lower panel) the p-values remain substantially constant while the p-value of the five minute sample deteriorates and the hypothesis is rejected. This suggests that the finite sample is able to reproduce theoretical properties of when the price observations are more than one per minute.


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

Mancino ME, Recchioni MC - PLoS ONE (2015)

Empirical distribution of the normalized asymptotic error for various sampling intervals.The panels show the empirical distribution of  for t ≈ 0.5 and c = 1/2 using 1-second returns (left upper panel), 30-second returns (right upper panel), 1-minute returns (left lower panel) 5-minute returns (right lower panel).
© Copyright Policy
Related In: Results  -  Collection

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

pone.0139041.g002: Empirical distribution of the normalized asymptotic error for various sampling intervals.The panels show the empirical distribution of for t ≈ 0.5 and c = 1/2 using 1-second returns (left upper panel), 30-second returns (right upper panel), 1-minute returns (left lower panel) 5-minute returns (right lower panel).
Mentions: We also try to determine the largest price frequency still capable of fitting satisfactorily the theoretical distribution prescribed by Theorem 3.1. We repeat the previous experiment choosing the Nyquist frequency N = n/2 and which are shown to reduce the variance and a sampling interval of ten seconds (i.e. n = 23400/10), thirty seconds (i.e. n = 23400/30), one minute (i.e. n = 23400/60) and five minutes (i.e. n = 23400/300). We evaluate the empirical distribution at t ≈ 0.5 and we apply the Bera-Jarque test at the significance level of 0.05. The empirical and theoretical distributions are shown in Fig 2. We can observe that when the sampling interval increases from ten seconds to one minute (upper panels and left lower panel) the p-values remain substantially constant while the p-value of the five minute sample deteriorates and the hypothesis is rejected. This suggests that the finite sample is able to reproduce theoretical properties of when the price observations are more than one per minute.

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