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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

Volatility signature plots versus sampling frequency in seconds.The graphs show the signature plots of illiquid market data on March 4-7, 2013.
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pone.0139041.g005: Volatility signature plots versus sampling frequency in seconds.The graphs show the signature plots of illiquid market data on March 4-7, 2013.

Mentions: In this subsection we consider the first data-set of U.S. S&P 500 index 5-second returns observed on March 4-7, 2013. We first carry out a preliminary analysis to study the main features of the observed data. This analysis is conducted through the volatility signature plot and the autocorrelation functions. Fig 5 shows the volatility signature plots corresponding to March 4, 5, 6 and 7, 2013 evaluated using the Realized Volatility (RV) and the Fourier estimator for integrated volatility. Roughly speaking, the volatility signature plots of Fig 5 are plots of the realized variance against sampling intervals and, as explained in Ref. [25], these sampling intervals are chosen to be multiples of the smallest sampling interval. Ref. [25] highlights that highly liquid assets display the largest realized variance estimates at the highest sampling rates (i.e. 5-second returns) while illiquid assets display the largest realized variance estimates at the lowest sampling rates (i.e. 20-minute returns). In fact, liquid assets show a negative serial autocorrelation so that the oscillating swings in the returns reduce for larger sampling intervals by the effect of cancelation. The signature plots illustrated in Fig 5 show that we are dealing with an illiquid asset.


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

Mancino ME, Recchioni MC - PLoS ONE (2015)

Volatility signature plots versus sampling frequency in seconds.The graphs show the signature plots of illiquid market data on March 4-7, 2013.
© Copyright Policy
Related In: Results  -  Collection

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

pone.0139041.g005: Volatility signature plots versus sampling frequency in seconds.The graphs show the signature plots of illiquid market data on March 4-7, 2013.
Mentions: In this subsection we consider the first data-set of U.S. S&P 500 index 5-second returns observed on March 4-7, 2013. We first carry out a preliminary analysis to study the main features of the observed data. This analysis is conducted through the volatility signature plot and the autocorrelation functions. Fig 5 shows the volatility signature plots corresponding to March 4, 5, 6 and 7, 2013 evaluated using the Realized Volatility (RV) and the Fourier estimator for integrated volatility. Roughly speaking, the volatility signature plots of Fig 5 are plots of the realized variance against sampling intervals and, as explained in Ref. [25], these sampling intervals are chosen to be multiples of the smallest sampling interval. Ref. [25] highlights that highly liquid assets display the largest realized variance estimates at the highest sampling rates (i.e. 5-second returns) while illiquid assets display the largest realized variance estimates at the lowest sampling rates (i.e. 20-minute returns). In fact, liquid assets show a negative serial autocorrelation so that the oscillating swings in the returns reduce for larger sampling intervals by the effect of cancelation. The signature plots illustrated in Fig 5 show that we are dealing with an illiquid asset.

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