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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 for various sampling intervals on January 27, 2001.Upper left panel (5.67-second returns), upper right panel (15-second returns), lower left panel (30-second returns) and lower right panel (1-minute returns).
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pone.0139041.g012: Autocorrelation for various sampling intervals on January 27, 2001.Upper left panel (5.67-second returns), upper right panel (15-second returns), lower left panel (30-second returns) and lower right panel (1-minute returns).

Mentions: Fig 10 shows the volatility signature plots corresponding to January 27, 28, 29 and 30, 2001 evaluated using the Realized Variance (RV) and the Fourier estimator for the integrated volatility. The four plots in Fig 11 show the autocorrelation functions corresponding to the 5.67-second returns on January 27-30, 2001. We can see that the first-order autocorrelation is significantly negative while the second and third autocorrelations are slightly positive. The blue lines denote the 95% confidence interval. The shape of the signature plot of Fig 10 and the negative first order autocorrelation in Fig 11 show that FIB30 returns are liquid data. Fig 12 shows the autocorrelation function of the returns on January 27, 2001 for four different sampling frequencies (i.e. upper left panel 5.67-second returns, upper right panel 15-second returns, lower left panel 30-second returns and lower right panel 1-minute returns). As in Subsection 5.1, the preliminary analysis suggests the use of 1-minute returns to sample the standardized return, . Furthermore, the simple test illustrated in Section 4.2 selects the frequencies N = n/2 and . Fig 13 shows the empirical distributions of the 1-minute standardized returns compared with the Gaussian density function obtained using illiquid data (Fig 13 left panel) and liquid data (Fig 13 right panel). The comparison of left and right panels highlights that the Fourier estimator provides accurate spot volatility estimates for both liquid and illiquid data. This is confirmed also by the VaR predictions shown in Table 5 (Liquid Data column), where the VaR predictions have at least two correct significant digits. Note that VaR predictions obtained using the TS estimators slightly outperform those obtained with Fourier estimator in the case of liquid data while the opposite happens in the case of illiquid data.


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

Mancino ME, Recchioni MC - PLoS ONE (2015)

Autocorrelation for various sampling intervals on January 27, 2001.Upper left panel (5.67-second returns), upper right panel (15-second returns), lower left panel (30-second returns) and lower right panel (1-minute returns).
© Copyright Policy
Related In: Results  -  Collection

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

pone.0139041.g012: Autocorrelation for various sampling intervals on January 27, 2001.Upper left panel (5.67-second returns), upper right panel (15-second returns), lower left panel (30-second returns) and lower right panel (1-minute returns).
Mentions: Fig 10 shows the volatility signature plots corresponding to January 27, 28, 29 and 30, 2001 evaluated using the Realized Variance (RV) and the Fourier estimator for the integrated volatility. The four plots in Fig 11 show the autocorrelation functions corresponding to the 5.67-second returns on January 27-30, 2001. We can see that the first-order autocorrelation is significantly negative while the second and third autocorrelations are slightly positive. The blue lines denote the 95% confidence interval. The shape of the signature plot of Fig 10 and the negative first order autocorrelation in Fig 11 show that FIB30 returns are liquid data. Fig 12 shows the autocorrelation function of the returns on January 27, 2001 for four different sampling frequencies (i.e. upper left panel 5.67-second returns, upper right panel 15-second returns, lower left panel 30-second returns and lower right panel 1-minute returns). As in Subsection 5.1, the preliminary analysis suggests the use of 1-minute returns to sample the standardized return, . Furthermore, the simple test illustrated in Section 4.2 selects the frequencies N = n/2 and . Fig 13 shows the empirical distributions of the 1-minute standardized returns compared with the Gaussian density function obtained using illiquid data (Fig 13 left panel) and liquid data (Fig 13 right panel). The comparison of left and right panels highlights that the Fourier estimator provides accurate spot volatility estimates for both liquid and illiquid data. This is confirmed also by the VaR predictions shown in Table 5 (Liquid Data column), where the VaR predictions have at least two correct significant digits. Note that VaR predictions obtained using the TS estimators slightly outperform those obtained with Fourier estimator in the case of liquid data while the opposite happens in the case of illiquid data.

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